OPINION

ROTH, Circuit Judge.

The Mead Corporation appeals several orders of the United States District Court for the Western District of Pennsylvania in a CERCLA contribution action brought by Beazer East, Inc. The main issue presented in these appeals is whether the District Court, over Mead's objection, properly referred part of Beazer's action — the equitable allocation proceeding — to the Magistrate Judge. In conducting this proceeding, the Magistrate Judge resolved factual disputes going to one of the ultimate issues in the case — what share of Beazer's response costs should be borne by each of the responsible parties — and, in doing so, essentially tried part of the case. Magistrate judges may not, however, try cases without the parties' consent. Because we conclude that the District Court's referral was an improper delegation of its traditional adjudicatory function, this case must be remanded for a new equitable allocation proceeding before the District Judge.

II. Factual Background and Procedural History

This is the second time this CERCLA contribution action has been before us. See Beazer East, Inc. v. The Mead Corp., 34 F.3d 206 (3d Cir. 1994) (" Beazer I"). In 1991, Beazer East, Inc., signed an Administrative Order on Consent (AOC) developed by the United States Environmental Protection Agency. The AOC required Beazer to investigate and cleanup the Woodward Facility Coke Plant, an industrial site in Alabama formerly owned and operated by Beazer. Beazer's predecessor, Koppers Company, Inc (KCI), bought the site from The Mead Corporation in 1974. Beazer sought contribution for its investigation and cleanup costs from Mead under CERCLA, 42 U.S.C. §§ 9607(a) 9613(f). Mead filed a counterclaim for indemnity based on certain provisions of the 1974 purchase agreement. The District Court granted summary judgment to Mead on this basis, but we reversed in Beazer I. We held that the key environmental indemnification provision failed the basic rule of Alabama contract law that promises to indemnify must be plain and unambiguous. Beazer I at 216-19. Accordingly, we remanded the case to the District Court for further proceedings on Beazer's contribution claim. Id. at 219 n. 10.

The chief tasks on remand were to determine which of Beazer's response costs were necessary and consistent with the National Contingency Plan (NCP), 42 U.S.C. 9607(a)(4)(B), and what percentage of those costs should be born by each of the responsible parties: Beazer, Mead, and Koppers Industries, Inc. (KII). 42 U.S.C. § 9613(f)(1) ("In resolving contribution claims, the court may allocate response costs among liable parties using such equitable factors as the court determines are appropriate"). In July 1996, the District Court referred this second question to the Magistrate Judge, ordering the Magistrate Judge to issue a report, "after a hearing if necessary," identifying the appropriate equitable factors and setting forth an allocation of Beazer's clean-up costs among the parties.

Mead objected, arguing that the Magistrate Judge did not have authority under the Magistrates Act to decide the equitable allocation issue in the first instance without the parties' consent. The District Court rejected this argument, reasoning that equitable allocation was "essentially . . . a pretrial matter" which can be referred to a magistrate judge without the parties' consent per 28 U.S.C. § 636(b)(1), and that any concerns over the Magistrate Judge's authority were allayed by the District Court's retention of de novo review over the Magistrate Judge's Report and Recommendation.

The Magistrate Judge conducted a lengthy hearing on the equitable allocation issue in May 1997 and ultimately issued a Report and Recommendation in November 1999. Starting from the premise that responsible parties should pay according to their relative fault, the Magistrate Judge found that Mead was responsible for disposing of approximately 90% of the waste on the site, while Beazer and KII together were responsible for disposing of approximately 10% of the waste. However, the Magistrate Judge adjusted this initial allocation to account for his proposed finding that the parties to the 1974 purchase agreement "intended that Mead be able to 'walk away' from the site, i.e., that Mead would not indemnify [KCI] for any future costs at the site for any reason, including environmental response costs." The Magistrate Judge proposed that Mead's share of Beazer's response costs be reduced and Beazer's share increased by 15% of the total costs. The Magistrate Judge also found that KII should bear a minor share of the response costs because, as the current owner, it would benefit from the environmental remediation of the site. The Magistrate Judge proposed that KII's share of Beazer's response costs should be 2.5%, that Mead's share should be 73.75% (90% of the waste minus 15% shifted to Beazer minus 1.25%, half of KII's share), and that Beazer's share should be 23.75% (10% of the waste plus 15% shifted from Mead minus 1.25%).

Following Mead's objections, in March 2000, the District Court adopted the Magistrate Judge's report with the following minor modifications: 1) 20% of the total costs — rather than 15% — would be shifted to Beazer based on the text, parole evidence, and legal context of the 1974 purchase agreement; and 2) KII's share would be subtracted entirely from Mead's share and added to Beazer's share because Beazer did not bring a contribution claim against KII. Accordingly, Mead's share was reduced to 67.5% (90% minus 20% minus 2.5%), and Beazer's increased to 32.5% (10% plus 20% plus 2.5%).

In February 2002, the District Court conducted a three-day trial to determine which of Beazer's actual costs incurred through December 31, 1999, were recoverable CERCLA response costs. In August 2002 the District Court issued a thorough opinion largely rejecting Mead's challenges to Beazer's costs. The court determined that Beazer had incurred recoverable response costs of $4,805,137.60 through the end of 1999 and entered judgment against Mead for 67.5% of this amount, or $3,243,467.80. Pursuant to the parties' stipulation, in September 2002, the Court further ordered Mead to pay pre-judgment interest in the amount of $1,538,164.03. Finally, in October 2002, the District Court entered a declaratory judgment requiring Mead to pay 67.5% of Beazer's ongoing response costs associated with implementing the AOC. The order also provided a framework for resolution of disputes over the necessity and NCP-consistency of such costs.

Mead timely appealed these orders. In December 2002, we assigned the case for mediation pursuant to the Third Circuit's Appellate Mediation Program, L.A.R. 33.0. The parties strenuously dispute what transpired at the February 26, 2003, mediation session. Beazer claims that the parties reached an oral agreement while Mead claims that the tentative agreement reached at mediation was conditioned on further management approval which was ultimately denied. In May 2003, Beazer moved this Court to enforce the alleged oral settlement and dismiss Mead's appeal with prejudice. The motion was referred to this panel and we decide it here along with Mead's appeals.

III. Jurisdiction

The District Court had jurisdiction over this case under 42 U.S.C. § 9613(b), which vests exclusive jurisdiction of CERCLA claims in the federal courts, as well as under 28 U.S.C. §§ 1331 and 1332. Horsehead Industries, Inc. v. Paramount Communications, Inc., 258 F.3d 132, 140 (3d Cir. 2001); Beazer I, 34 F.3d at 210. We have appellate jurisdiction over the appeal from the District Court's final orders described above pursuant to 28 U.S.C. § 1291. Horsehead Industries, 258 F.3d at 140. Finally, we have original jurisdiction over Beazer's motion to enforce the alleged settlement agreement. See Fed.R.App.Pro. 33 ("The court may, as a result of the [mediation], enter an order controlling the course of the proceedings or implementing any settlement agreement."). See also Herrnreiter v. Chicago Housing Auth., 281 F.3d 634, 637 (7th Cir. 2002).

V. Discussion

A. Enforcement of the alleged oral settlement.

Beazer's motion to specifically enforce the alleged oral settlement reached at the appellate mediation and to dismiss this appeal with prejudice must be rejected. Both Local Appellate Rule (LAR) 33.5 and sound judicial policy compel the conclusion that parties to an appellate mediation session are not bound by anything short of a written settlement. Any other rule would seriously undermine the efficacy of the Appellate Mediation Program by compromising the confidentiality of settlement negotiations.

Beazer requests enforcement of the alleged oral settlement but admits that there are genuine factual disputes regarding whether the parties actually reached an agreement. Mead correctly argues that we cannot resolve these disputes without violating the confidentiality rule, LAR 33.5(c). With exceptions not relevant here, Rule 33.5(c) provides that no one at the mediation session — neither mediator, counsel, nor party — may disclose "statements made or information developed during the mediation process." The provision further provides that "the parties are prohibited from using any information obtained as a result of the mediation process as a basis for any motion or argument to any court." LAR 33.5(c) (emphases added). Beazer cannot prove the existence or terms of the disputed oral settlement without violating this provision's broadly stated prohibitions.

Beazer argues that the rule is not so sweeping. Beazer concedes that it may not use information obtained at the conference in any argument going to the merits of the appeal, but contends that it must be able to use that information for the limited purposes of proving the existence and terms of a settlement. This argument is unpersuasive. First, the rule is stated in the broadest possible language and does not contemplate any such exception. Second, Beazer's proposed exception would effectively undermine the rule and would compromise the effectiveness of the Appellate Mediation Program. A confidentiality provision "permits and encourages counsel to discuss matters in an uninhibited fashion often leading to settlement." Lake Utopia Paper Ltd. v. Connelly Containers, Inc., 608 F.2d 928, 929 (2d Cir. 1979). If counsel know beforehand that the proceedings may be laid bare on the claim that an oral settlement occurred at the conference, they will "of necessity . . . feel constrained to conduct themselves in a cautious, tight-lipped, non-committal manner more suitable to poker players in a high-stakes game than to adversaries attempting to arrive at a just resolution of a civil dispute." Id.; see also Herrnreiter, 281 F.3d at 637 ("A motion to implement a conference settlement easily could be a strategy to pierce the confidentiality of the negotiations and inform the judges of the parties' position, rather than to carry out an agreement actually reached."). Third, Beazer's proposed exception would require appellate courts to receive evidence and resolve factual disputes, tasks more properly suited to the district courts. See Herrnreiter, 281 F.3d at 637.

We must also consider LAR 33.5(d), which provides that "[n]o party shall be bound by statements or actions at a mediation session unless a settlement is reached." The rule further provides that "if a settlement is reached, the agreement shall be reduced to writing and shall be binding upon all parties to the agreement." Mead argues that the most "straightforward" reading of this rule is that no agreement is binding until it is written. Mead's reading is serial: 1) if the parties reach an agreement, 2) then that agreement shall be written down, and 3) then, and only then, the agreement shall be binding. However, the grammatical structure of the rule is consistent with a parallel construction: 1) if the parties reach an agreement, 2)a) then it shall be reduced to writing, and, 2)b) then it shall be binding. Under this reading, the agreement is binding because it has been reached, not because it has been written down.

The "parallel" construction of Rule 33.5(d) — which would make oral settlement agreements binding on the parties — is irreconcilable with Rule 33.5(c), because, as described above, there is no way to prove the existence or terms of a disputed oral settlement without violating the confidentiality provision. Therefore, we adopt Mead's "serial" reading of Rule 33.5(d), according to which an agreement is not binding unless it is reduced to writing. We note that the Ninth Circuit adopted a serial interpretation of similar language in Barnett v. Sea Land Serv., Inc., 875 F.2d 741, 743-44 (9th Cir. 1989).

Further, Judge Easterbrook's opinion in Herrnreiter provides persuasive policy justifications for requiring written settlements. In Herrnreiter the parties admitted that they had reached an oral settlement at a voluntary appellate mediation session but they did not agree on the terms. Id. at 636. The court denied the defendant's motion to implement the oral settlement. Id. at 637. The court noted that there is no transcript of appellate mediation sessions and that settlement conference attorneys presiding over such sessions promise both sides that nothing that transpires at the conference will be revealed to the judges; the court finally observed that appellate courts are not well-positioned to conduct fact-finding missions. Id. Accordingly, the court concluded that nothing short of a mutually satisfactory written settlement agreement could terminate an appeal. Id. "Any other approach would compromise the confidentiality of the negotiations, require the settlement attorneys to become witnesses in appellate factfinding proceedings, and substantially complicate the disposition of litigation." Id. All of these concerns are equally present in this case. In fact, the argument for preserving confidentiality of proceedings is even stronger in this case, where participation in the appellate mediation program is mandatory and the mediation is directed by a court-employed mediator or a judicial officer. See In re Anonymous, 283 F.3d 627, 636-37 (4th Cir. 2002) (citation omitted).

Beazer complains that if Mead's interpretation of Rules 33.5(c) and (d) is accepted then parties will be able to enter into oral agreements at settlement conferences and simply back out on a whim, significantly deterring the federal policy of encouraging settlements. See D.R. v. East Brunswick Bd. of Educ., 109 F.3d 896, 901 (3d Cir. 1997). Beazer also relies on our oft-repeated position that a written agreement is not necessary to render a settlement enforceable. See, e.g., Green v. John H. Lewis Co., 436 F.2d 389, 390 (3d Cir. 1970) (citations omitted). Mead's first argument is simply incorrect: if parties know beforehand that only a written settlement agreement is binding, they will be sure to memorialize their agreement in writing at the end of the mediation session. Its second argument is based on basic common law contract principles, see Main Line Theatres, Inc. v. Paramount Film Distributing Corp., 298 F.2d 801, 803 (3d Cir. 1962), and has no application where specific court rules provide otherwise.

For all these reasons, Beazer's motion to enforce the alleged oral settlement agreement and dismiss the appeal is denied.

B. The District Court's Referral to the Magistrate Judge.

Mead argues that the Magistrates Act, 28 U.S.C. § 636, does not authorize the District Court's referral to the Magistrate Judge, over Mead's objection, of the equitable allocation issue. Mead contends that, for that reason, the Magistrate Judge lacked jurisdiction to conduct a hearing or issue a Report and Recommendation. Mead further asserts that, because the Magistrate Judge lacked jurisdiction, the District Court's putative de novo review did not rectify the improper referral. We agree with Mead on both points.

The jurisdiction of magistrate judges is limited by statute and may not be augmented by the federal courts. See Thomas v. Whitworth, 136 F.3d 756, 758 (11th Cir. 1998) (citing NLRB v. A-Plus Roofing, Inc., 39 F.3d 1410, 1415 (9th Cir. 1994)). The District Court did not rely on any specific provision of the Magistrates Act in its order of referral or its order rejecting Mead's objections to the referral, but it is clear from the context that the court considered the equitable allocation issue a "pretrial matter" under § 636(b)(1). Beazer argues in the alternative that the referral could be re-characterized as a designation of the Magistrate Judge to serve as a special master under § 636(b)(2) and Federal Rule of Civil Procedure 53(b). Beazer also argues that the referral was permissible under § 636(b)(3), which authorizes magistrate judges to undertake "such additional duties as are not inconsistent with the Constitution and laws of the United States." We conclude that the referral was not proper under any provision of the Magistrates Act. 1. Equitable allocation is not a "pretrial matter."

We first consider whether the equitable allocation proceeding referred to the Magistrate Judge is correctly characterized as a "pretrial matter." The Magistrates Act authorizes district courts to appoint magistrate judges to consider pretrial matters without regard to the parties' consent. 28 U.S.C. § 636(b)(1). The District Court considered the equitable allocation proceeding a pretrial matter because it constituted a "significant step" in resolving the case:

First, the identification of the equitable factors that will be relevant in an ultimate disposition of this case essentially is a pretrial matter and constitutes a significant step in resolving the parties' current dispute. In addition, submitting briefs in support of an allocation of Beazer's clean-up costs among the parties likewise is a pretrial undertaking which is necessary to narrow the issues for trial.

The District Court's reasoning is misleading and without supporting authority. First, the District Court significantly understates the significance and scope of the referral. The parties did not simply "submit briefs" in support of the equitable allocation issue — they presented extensive testimonial and documentary evidence over the course of a 12-day hearing. At the conclusion of this hearing the Magistrate Judge not only identified equitable factors but also applied those factors to make a recommendation as to the allocation of liability among the parties. Second, by the District Court's reasoning, any issue in the case could be could be considered by a magistrate judge in a "pretrial" proceeding so long as the Court later conducted a "trial" on at least one issue. Whether a given issue is a "pretrial matter," however, turns on the nature of the issue itself, not on the position in which it falls in the sequence of decision.

A CERCLA contribution action consists of determining which parties are liable under CERCLA and apportioning the liable parties' shares in an equitable manner. See 42 U.S.C. §§ 9607(a) 9613(f)(1); New Jersey Turnpike Authority v. PPG Industries, Inc., 197 F.3d 96, 104 n. 7 (3d Cir. 1999); Kalamazoo River Study Group v. Menasha Corp., 228 F.3d 648, 656-57 (6th Cir. 2000). Here, the first phase was uncontested: Mead, Beazer, and KII are each liable as current or former owners and operators of the Woodward Coke Plant. See 42 U.S.C. § 9607(a)(1). The equitable apportionment phase was divided into two proceedings: a proceeding (conducted by the Magistrate Judge) to determine the parties' equitable shares of response costs on a percentage basis, see 42 U.S.C. § 9613(f)(1), and a separate proceeding (conducted by the District Court) to determine which of Beazer's actual costs qualify as recoverable response costs, see 42 U.S.C. § 9607(a)(4)(B). Contrary to the District Court's assertions, then, the issue referred to the Magistrate Judge was not a precursor to resolution of the ultimate issue — it was one of the ultimate issues to be tried. In fact, it was the only issue in the case unique to contribution claims. Whether a party is liable and which costs are recoverable are questions governed by CERCLA's liability provision, 42 U.S.C. § 9607. The contribution provision, section 9613(f)(1), provides that "[i]n resolving contribution claims, the court may allocate response costs among liable parties using such equitable factors as the court determines are appropriate." This was the very task referred to the Magistrate Judge.

Further, this task required the Magistrate Judge to resolve factual disputes going to the merits of the case. In Banks v. United States, 614 F.2d 95 (6th Cir. 1980), the court reasoned that section 636(b)(1) was carefully drafted to avoid granting magistrate judges the authority to perform fact-finding on the merits of case because that function is the essence of a trial, and magistrate judges cannot conduct trials without the parties' consent:

The statute clearly contemplates that a magistrate be allowed to help a district judge with a variety of pre-trial motions. However, absent consent, the magistrate cannot conduct a trial itself. Under our system of law, when there are factual controversies, there must be a trial. Only when a party is entitled to judgment as a matter of law may a trial be aborted. See e.g. Fed R. Civ. P. 12, 56. Congress was careful to recognize this distinction when it amended the Federal Magistrate's Act. The Act permits a magistrate to prepare proposed findings on a variety of "case dispositive" motions such as summary judgment. Except for prisoner's cases, the act does not permit the magistrate to perform fact-finding on the merits of a case. That is the exclusive function of a district judge. Indeed, the magistrate judge's role is to free the judge from pre-trial wrangling so that he can try cases.

Id. at 97. In this case the Magistrate Judge did not facilitate the District Court's ultimate adjudicatory function — he assumed that function. In the course of making his Report and Recommendation, the Magistrate Judge resolved two critical factual disputes. First, the he determined that Mead was responsible for approximately 90% of the waste at the Woodward Coke Plant. Second, he found that the parties to the 1974 purchase agreement intended that Mead would not be responsible for any environmental liabilities at the Plant. By making these findings, he tried part of the case and usurped the role of the District Judge. Accordingly, the equitable allocation proceeding conducted by the Magistrate Judge is not a "pretrial matter" under 28 U.S.C. § 636(b)(1).

One further argument warrants mention. Beazer and the District Court imply that the equitable allocation proceeding conducted by the Magistrate Judge was a "pretrial matter" simply because it preceded the recoverable costs proceeding conducted by the District Court. This is mere happenstance. The proceedings could have been held in the reverse order or held together. As discussed above, the important issue is not the order of decision but the nature of decision — both the equitable allocation proceeding and the recoverable costs proceeding required the decisionmaker to resolve factual disputes going to the ultimate issues in the case.

2. Equitable allocation cannot be referred to a special master without the parties' consent.

Beazer argues that, even if the referral is not authorized by § 636(b)(1), we should recharacterize the referral as a designation of the Magistrate Judge to serve as a special master under § 636(b)(2). We need not reach the issue of whether an appellate court can save a flawed referral in this manner because we hold that the designation of a Magistrate Judge to conduct an equitable allocation without the parties' consent would constitute an abuse of discretion. See Sierra Club v. Clifford, 257 F.3d 444, 446 (9th Cir. 2001) (designation of special master is reviewed for abuse of discretion); American Cyanamid Co. v. Ellis-Foster Co., 298 F.2d 244, 247 (3d Cir. 1962) (same).

Section 636(b)(2) provides in pertinent part that a judge "may designate a magistrate judge to serve as a special master pursuant to the applicable provisions of this title and the Federal Rules of Civil Procedure" without the parties' consent. The applicable Federal Rule is Rule 53(b), which provides for references to special masters:

A reference to a master shall be the exception and not the rule. In actions to be tried by a jury, a reference shall be made only when the issues are complicated; in actions to be tried without a jury, save in matters of account and of difficult computation of damages, a reference shall be made only upon a showing that some exceptional condition requires it.

The non-jury standard of review applies here. Thus, unless the proceeding referred to the Magistrate Judge in this case is characterized as part of a "difficult computation of damages," the reference can only be justified upon a showing that some "exceptional condition" required it.

Beazer makes no argument that any "exceptional condition" exists in this case, nor does Beazer argue that the Magistrate Judge performed any difficult computations. Rather, Beazer contends that the referral was proper because the equitable allocation proceeding conducted by the Magistrate Judge was a "predicate" to a "difficult computation of damages" performed by the District Court. Beazer's expansive reading of Rule 53(b) is at odds with the Supreme Court's restrictive interpretation.

In La Buy v. Howes Leather Co., 352 U.S. 249, 256, 259, 77 S.Ct. 309, 1 L.Ed.2d 290 (1957), the Court affirmed the appellate court's issuance of a writ of mandamus compelling the District Court to vacate its order referring essentially the entirety of two complex antitrust cases to a special master. The Court noted that while masters could "aid judges" in the performance of specific duties, they could not be permitted to "displace the court." Id. at 256, 77 S.Ct. 309; see also Prudential Ins. Co. v. United States Gypsum Co., 991 F.2d 1080, 1086 (3d Cir. 1993) ("A district court has no discretion to delegate its adjudicatory responsibility in favor of a decision maker who has not been appointed by the President and confirmed by the Senate.") (citing La Buy); In re Bituminous Coal Operators' Ass'n, Inc. 949 F.2d 1165, 1168 (D.C. Cir. 1991) ("Rule 53 . . . authorizes the appointment of special masters to assist, not to replace, the adjudicator, whether judge or jury, constitutionally indicated for federal court litigation"). The Court found that the references at issue "amounted to little less than an abdication of the judicial function depriving the parties of a trial before the court on the basic issues involved in the litigation." La Buy, 352 U.S. at 256, 77 S.Ct. 309. The Court acknowledged, however, that difficult damages computations could sometimes be referred to a master without the parties' consent. "The detailed accounting required to determine the damages suffered by each plaintiff might be referred to a master after the court has determined the over-all liability of defendants, provided the circumstances indicate that the use of the court's time is not warranted in receiving the proof and making the tabulation." Id. at 259, 77 S.Ct. 309.

Accountings and other damages computations may be referred without the parties' consent because they generally do not call for any peculiar judicial talent or insight. See 9A Charles Alan Wright Arthur R. Miller, Federal Practice and Procedure § 2605 at 655-66 (2d ed. 1994). Equitable apportionment, on the other hand, is a quintessentially judicial endeavor. CERCLA's contribution provision authorizes the court to "allocate response costs among liable parties using such equitable factors as the court determines are appropriate." 42 U.S.C. § 9613(f)(1). In a given case, "a court may consider several factors or a few, depending on the totality of the circumstances and equitable considerations." New Jersey Turnpike Authority v. PPG Industries, Inc., 197 F.3d 96, 104 (3d Cir. 1999) (citation omitted). This flexible inquiry involves discretion, judgment, and legal reasoning that simply is not connoted by the phrase "difficult computation of damages." This case provides a good illustration of this point.

The Magistrate Judge's proposed allocation turned chiefly on three factors: 1) volume of waste should be the pre-eminent equitable factor given CERCLA's over-arching "polluter-pays" principle; 2) Mead was responsible for approximately 90% of the waste; and 3) Mead was nonetheless entitled to a reduction in its share based on the parties' intent that Mead would not be responsible for future environmental liabilities. In weighing these factors, only the second is reasonably related to a "computation of damages." The other two turn on questions of law, policy, equity, and contractual intent. Further, even with respect to weighing the second factor, the computations performed by the Magistrate Judge were not "difficult" — they entailed elementary subtraction and addition of percentages. The Magistrate Judge did not crunch any numbers to determine that Mead was responsible for 90% of the waste on the site; rather, he decided which expert's percentage estimates were more convincing. In fact, even this decision largely turned on a legal question: should Beazer be able to recover all of its response costs based on an AOC ordered under the Resource Conservation and Recovery Act that required investigation and monitoring of the entire industrial site, or should it be limited, as Mead's chief expert contended, to costs that would have been assessed under a more modest hypothetical AOC issued pursuant to CERCLA? Thus, the issues referred to the Magistrate Judge here were not akin to a complicated accounting or difficult damages calculation. Rather, they were foremost among the "basic issues" to be tried, and the District Court's referral of those issues without the parties' consent was "an abdication of the judicial function." La Buy, 352 U.S. at 256, 77 S.Ct. 309.

Beazer also argues that our opinion in Beazer I ended the "liability phase" of this case, that everything that occurred on remand constituted the "damages phase," and therefore everything on remand could have been properly referred to a master. This formalistic argument is inconsistent with La Buy's reasoning. In United States v. Microsoft Corp., 147 F.3d 935, 954-55 (D.C. Cir. 1998), the D.C. Circuit Court of Appeals vacated a reference to a special master to determine the parties' rights under a complex consent decree. Seeking to uphold the reference, the Department of Justice invoked the "well-established tradition" allowing special masters to oversee compliance during the remedial phase of litigation, arguing that the reference to oversee implementation of the consent decree fell squarely within that tradition. Id. at 954. (citations omitted). The court rejected this position, holding that "[t]he matters referred to the master are no more "remedial" than would be those of any total referral of a contract case. The concern about nonconsensual references turns on the determination of rights, not on a formalistic division of the juridical universe into pre-trial, trial and post-trial. It is for this reason that special masters may not decide dispositive pretrial motions." Id. (citation omitted). Similarly, the reference here involved a complex and delicate determination of equities.

We note, however, that there is some support for Beazer's position. In United States v. Conservation Chemical Co., 106 F.R.D. 210, 216 (W.D.Mo. 1985), the District Court referred all pretrial and discovery matters as well as the trial on the merits to a special master without the parties' consent. The reference included "the authority to hold hearings and issue recommendations on the claims for . . . apportionment of costs." Id. Predictably, the Eighth Circuit Court of Appeals held that no "exceptional condition" justified the District Court's sweeping reference. In re Armco, 770 F.2d 103, 105 (8th Cir. 1985). But then, without explaining its reasoning, the court affirmed all aspects of the reference except for the trial on the liability issues. Thus, the court affirmed reference of all post-liability damages proceedings. Id. Although not explicitly stated, this reference necessarily covered any equitable allocation proceedings that might be necessary to resolve contribution claims brought by any of the liable parties.

The Armco Court's unexplained decision to uphold the reference of dispositive matters without any showing of exceptional conditions has been met with perplexity by two other circuit courts. Stauble v. Warrob, Inc., 977 F.2d 690, 696 (1st Cir. 1992) (noting that the court was "baffled" by the Armco Court's decision to authorize reference of dispositive pre-trial motions); In re United States, 816 F.2d 1083, 1091 (6th Cir. 1987) (noting the court's inability "to follow the [ Armco] Court's reasoning" on this issue). We also do not consider Armco to be persuasive authority. It is possible that the Armco Court was overly solicitous towards the District Court's Rule 53(b) reference because it perceived that the District Court required an extraordinary degree of flexibility to handle an enormous CERCLA case involving more than 250 parties. See 9A Wright Miller, Federal Practice and Procedure § 2605, at 666 ("Despite the restrictive standard set out in the La Buy case, the actual utilization of masters under Rule 53(b) in the past two decades has been quite lively[,] undoubtedly [in response to] the rapid growth of complex litigation in the federal courts, particularly in cases requiring significant scientific and technical knowledge, [and] management skills"). In contrast, this case does not present similar administrative challenges — there are only three parties, and one, KII, has played only a minor role in the proceedings.

Accordingly, we reject Beazer's contention that the District Court could have designated the Magistrate Judge to hear the equitable allocation issue as a special master without Mead's consent.

3. Equitable allocation cannot be referred under the "additional duties" clause.

Finally, we reject Beazer's suggestion that the referral was proper under the "additional duties" clause. 28 U.S.C. § 636(b)(3). This clause covers only subsidiary matters in the absence of the parties' consent, and equitable allocation is central, rather than subsidiary, to a CERCLA contribution action.

The parties' consent or lack thereof is a key factor in deciding whether a referral is authorized under the "additional duties" clause. In Gomez v. United States, 490 U.S. 858, 876, 109 S.Ct. 2237, 104 L.Ed.2d 923 (1989), the Court held that this clause did not authorize magistrate judges to supervise voir dire proceedings in a criminal case over a defendant's objection. However, in Peretz v. United States, 501 U.S. 923, 932-36, 111 S.Ct. 2661, 115 L.Ed.2d 808 (1991), the Court held that the "additional duties" clause did authorize the reference of voir dire in a criminal case where the defendant consented to the reference. The Court reasoned that the scope of the clause varied significantly according to whether the parties' consented to the reference. See Peretz, 501 U.S. at 931-33, 111 S.Ct. 2661; Gomez, 490 U.S. at 870-71, 109 S.Ct. 2237. As the Court explained in Gomez and reiterated in Peretz, the scope of § 636(b)(3)'s residuary clause had to be interpreted in light of the duties specifically authorized in the other sections of the Act. Peretz, 501 U.S. at 930-31, 111 S.Ct. 2661 (citing Gomez, 490 U.S. at 864, 109 S.Ct. 2237). The Court explained that "the duties that a magistrate judge may perform over the parties' objections are generally subsidiary matters not comparable to supervision of jury selection. However, with the parties' consent, a district judge may delegate to a magistrate judge supervision of entire civil and misdemeanor trials. These duties are comparable in responsibility and importance to presiding over voir dire at a felony trial." Peretz, 501 U.S. at 932, 111 S.Ct. 2661.

Thus, in the absence of Mead's consent, the referral would only be authorized under § 636(b)(3) if we characterized the equitable allocation proceeding as a "subsidiary matter." See 12 Charles Alan Wright, Arthur R. Miller Richard L. Marcus, Federal Practice Procedure § 3068.1 at 329 (2d ed. 1997). As explained in the previous two sections, equitable allocation is central to Beazer's CERCLA action, not subsidiary thereto. Accordingly, the referral could not be authorized under the "additional duties" clause over Mead's objection.

This conclusion is consistent with Congressional intent. As the Court in Peretz explained, "[t]he Act is designed to relieve the district courts of certain subordinate duties that often distract the courts from more important matters." 501 U.S. at 934, 111 S.Ct. 2661. In support of this assessment, the Court cited several statements from the legislative history of the Act and its various amendments. See, e.g., H.R. Rep. no. 94-1609, p. 7 (1976), U.S. Code Cong. Admin.News 1976, pp. 6162, 6167 (stating that a magistrate judge is to "assist the district judge in a variety of pre-trial and preliminary matters thereby facilitating the ultimate and final exercise of the adjudicatory function at the trial of the case"). Equitable allocation is at the very core of a CERCLA contribution action and is not a preliminary or subordinate matter.

4. Remand is required notwithstanding the District Court's purported de novo review.

Beazer contends, and the District Court reasoned, that any flaw in the referral is corrected by the District Court's purported de novo review of the Magistrate Judge's proposed equitable allocation. This argument is unavailing.

First, as noted above, a magistrate judge's authority is jurisdictional. Without the parties' consent, a magistrate judge cannot conduct a trial or any part thereof, see 28 U.S.C. § 636(c)(1) ("[u]pon the consent of the parties, a . . . magistrate judge . . . may conduct any or all proceedings in a jury or nonjury civil matter"), and "[t]he mere existence of a recommendation [and accompanying de novo review] will not change a full trial [or any part thereof] into a pre-trial motion." Jeffrey S. v. State Bd. of Educ., 896 F.2d 507, 512 n. 17 (11th Cir. 1990) (citing Hall v. Sharpe, 812 F.2d 644, 647 (11th Cir. 1987)). Second, § 636(b)(1)(B) provides that certain dispositive pre-trial motions may be referred to a magistrate judge, but the magistrate judge's proposal must be reviewed de novo by the court. Mead correctly argues that this provision would be meaningless if no specific statutory delegation were necessary so long as the District Court conducted a de novo review. Third, the District Court's error cannot be considered harmless no matter how admirable the Magistrate Judge's efforts may have been. See United States v. Ruiz-Rodriguez, 277 F.3d 1281, 1293 n. 17 (11th Cir. 2002) ("[H]armless error analysis does not apply when a magistrate judge lacks the power to act."). Since the Magistrate Judge lacked the power to conduct the equitable allocation proceeding in this case, there was nothing for the District Court to review.

Although the issue of appropriate remedy is less settled where the flawed referral is to a special master (or a magistrate judge acting as a special master) rather than to a magistrate judge qua magistrate judge, remand for a new trial is the proper remedy even if the District Court's referral could be re-characterized as a designation of the Magistrate Judge to serve as a special master. First, while at least two courts of appeals have suggested that a remand for a new trial may not be required where the district court reviews the master's report de novo, Sierra Club v. Clifford, 257 F.3d 444, 447 (9th Cir. 2001) (vacating reference but declining to decide whether de novo review by the district judge could save a flawed reference), Stauble, 977 F.2d at 698 n. 12 (same), we rejected a similar argument in Prudential. The District Court in Prudential had stated that the reference was limited to pre-trial motions, and that it would review every conclusion of law proposed by the special master de novo. 991 F.2d at 1086 n. 11. We reasoned, however, that de novo review of legal matters could not save an improper referral because such review was always available regardless of whether the referral violated Rule 53(b). Id. That is, if de novo review of legal issues cured referrals made in violation of Rule 53(b), that provision would be meaningless.

Furthermore, the referral in this case encompassed questions of fact as well as questions of law, and Rule 53(e)(2) provides that in non-jury trials the district court " shall accept the master's findings of fact unless clearly erroneous." Fed.R.Civ.Pro. 53(e)(2) (emphasis added); Apex Fountain Sales, Inc. v. Kleinfeld, 818 F.2d 1089, 1097 (3d Cir. 1987) (noting that review of master's legal conclusions is plenary, but that district court must accept master's factual findings unless clearly erroneous). Relying on this provision, the court in Microsoft rejected the argument that de novo review can save an improper referral because the master's factual conclusions cannot be reviewed de novo under Rule 53(e)(2). 147 F.3d at 955; see also Sierra Club, 257 F.3d at 448 (suggesting but not reaching same conclusion). In this case the District Court claims that it reviewed both the Magistrate Judge's factual findings and its legal conclusions de novo. This is inconsistent with Rule 53(e)(2), and a district court cannot cure one violation of Rule 53 by committing another. Finally, it would be inappropriate to re-characterize the referral as a flawed designation of a special master solely to avoid the remand required by case law construing other provisions of the Magistrates Act.

Accordingly, this case must be remanded for a new equitable allocation proceeding before the District Court. We note that Beazer's contribution action is now in its fourteenth year and will likely enjoy several more birthdays, partly because our reversal today will require the parties to retread well-worn ground. In an attempt to avoid further duplicative litigation and speed this case towards its conclusion, we take this opportunity to resolve two other issues raised by the parties on appeal.

C. The District Court's Equitable Allocation Was Erroneous.

First, we agree with Mead that the District Court committed legal error, and therefore abused its discretion, in prioritizing the parties' respective contributions of waste at the Woodward Coke Plant in determining the appropriate allocation of Beazer's response costs. The District Court found that the parties to the 1974 sale intended that Mead would not bear any environmental liability following the 1974 sale, but reduced Mead's equitable share by only 20% in recognition of this and related findings that we refer to here as the "purchase agreement factors," all of which favor Mead.

The District Court's decision to prioritize the volume of waste over the purchase agreement factors appears to follow two related rationales explicitly developed in the Magistrate Judge's Report and Recommendation. The Magistrate Judge concluded that "CERCLA is premised upon the policy that the 'polluter pays.'" Thus, the Magistrate Judge began from the premise that each party's equitable share should be driven by its respective contribution of waste. The Magistrate Judge deviated only slightly from this premise to account for the equitable factors surrounding the 1974 sale. The Magistrate Judge also concluded that it would be inconsistent with our decision in Beazer I to allocate "all or even most" of the response costs to Mead. The District Court somewhat ambiguously adopted each rationale. However, neither Beazer I, nor CERCLA itself, requires that the parties' intent to shift environmental risk be subordinated to the "polluter pays" principle — as long as someone pays. Therefore, the District Court's allocation, which was based in part on its agreement with the Magistrate Judge's flawed reasoning, was an abuse of discretion.

First, the Magistrate Judge's and District Court's prioritization of the "polluter pays" principle in equitable allocation proceedings is inconsistent with CERCLA's contribution provision. That provision authorizes the district courts to "allocate response costs among liable parties using such equitable factors as the court determines are appropriate." 42 U.S.C. § 9613(f)(1). Courts examining this language and its history have concluded that Congress intended to grant the district courts significant flexibility in determining equitable allocations of response costs, without requiring the courts to prioritize, much less consider, any specific factor. In a leading case, the Seventh Circuit Court of Appeals explained that "the language of section 9613(f) clearly indicates Congress's intent to allow courts to determine what factors should be considered in their own discretion without requiring a court to consider any particular list of factors." Environmental Transportation Systems, Inc. v. ENSCO, 969 F.2d 503, 508 (7th Cir. 1992); see also United States v. R.W. Meyer, Inc., 932 F.2d 568, 576-77 (6th Cir. 1991) (reasoning that section 9613(f)(1)'s language "confirms the legislative intent to grant courts flexibility in exercising their discretion") (citations to legislative history omitted). As we have held, "a court may consider several factors or a few, depending on the totality of the circumstances." New Jersey Turnpike Authority v. PPG Industries, Inc., 197 F.3d 96, 104 (3d Cir. 1999) (citation omitted).

Accordingly, the "polluter pays" principle has no canonical or transcendent importance under § 9613(f)(1); it is certainly not the "primary policy" of contribution claims, as implied by the District Court. It is simply one of many factors that may or may not bear on a given equitable allocation determination. See Kerr-McGee, 14 F.3d at 326 (listing possible factors). Specifically, there is no basis in CERCLA's text or history for prioritizing a priori the parties' relative contributions of waste over their contractual intent to allocate environmental liability among themselves. To the contrary, CERCLA expressly authorizes private indemnity agreements, see 42 U.S.C. § 9607(e)(1); Fisher Development Co. v. Boise Cascade Corp., 37 F.3d 104, 110 (3d Cir. 1994) (finding in § 107(e)(1) "a policy favoring private ordering of ultimate risk distribution"), and the District Court's insistence on elevating relative waste contribution is fundamentally inconsistent with CERCLA's policy of favoring private indemnity agreements.

Second, Beazer I dealt with the legal interpretation of Paragraph 4(c). As a matter of equity, however, the intent of the parties, which is manifested by their actions and in the written agreement, can be taken into account — no matter what our legal conclusion was in Beazer I. Beazer I does not tip the equitable scales one way or another. In Beazer I, we determined that the 1974 agreement was governed by Alabama law, 34 F.3d at 211-15, and that indemnification agreements are enforceable under Alabama law only if they contain "a plain and unambiguous expression of intent to cover the cost of the liability in question." Id. at 216. Applying this standard, we concluded that "nothing in this agreement demonstrates a clear and unambiguous intent to transfer all CERCLA liability to [KCI]." Id. at 219. The Magistrate Judge correctly reasoned that Beazer I reached no conclusion regarding the parties' actual intent; only that, as a matter of Alabama law, the contract did not contain a sufficiently clear expression that KCI would indemnify Mead against all environmental liability associated with the site. See id. Thus, the Magistrate Judge concluded that "there is no inherent inconsistency in the ruling made on appeal and a decision by this court that, as a matter of equity, the parties' intentions concerning indemnity, to the extent they can be divined from both the document and any other evidence offered by the parties, should be considered in equitable allocation."

However, the Magistrate Judge further reasoned that shifting all or most of the response costs to Beazer based on the purchase agreement factors "would give the agreement, found legally insufficient under Alabama law, the force of law, and would place [the District] Court's decision at odds with the ruling made by the Court of Appeals." This conclusion does not follow from Beazer I.

The District Court, however, rejected Mead's contention that the Magistrate Judge had misinterpreted Beazer I. The court quoted from its penultimate paragraph, seemingly for the proposition that Mead's "fair share" of Beazer's response costs should be greatly influenced, if not largely determined, by Mead's relative contributions of hazardous waste to the site. The penultimate paragraph provides:

Our refusal to construe Paragraph 4(c) as a clear promise by Beazer to indemnify Mead against CERCLA response costs leaves both Beazer and Mead responsible for their fair share of the cleanup costs associated with the Coke Plant. That result reinforces CERCLA policy. "Congress enacted CERCLA, a complex piece of legislation . . . to force polluters to pay for costs associated with remedying their pollution." United States v. Alcan Aluminum Corp. 964 F.2d 252, 258 (3d Cir. 1992).

34 F.3d at 219. Apparently, the District Court considered this quotation from Alcan Aluminum to support (or perhaps require) elevating the "polluter pays" principle above all other equitable factors.

The quoted paragraph does not warrant such significance. The first two sentences uncontroversially state that holding Mead and Beazer responsible for their fair share of cleanup costs reinforces CERCLA policy. Id. at 219. The next sentence, the quotation from Alcan Aluminum, is to the effect that Congress intended that polluters pay for the costs of remedying their pollution. Id. (quoting Alcan, 964 F.2d at 258). The District Court apparently inferred from the juxtaposition of these statements that each party's "fair share" must be more or less rigidly tied to its share of pollution at the site. Such an interpretation is, however, fundamentally at odds with CERCLA's contribution provision as well as with CERCLA's policy of favoring private indemnity agreements.

We note, moreover, that in the footnote at the end of the penultimate paragraph, the Beazer I Court quoted the "equitable factors" language of section 9607(a) and went on to note that on remand, "the trial court will have to revisit the parties' contribution claims and correspondingly apportion liability for attendant CERCLA response costs." This direction is significantly broader than a direction that liability should be apportioned to reflect each party's share of pollution at the site — which the Beazer I Court could easily have stated if that were its intent.

It is clear, then, that the District Court erred in eliminating significant consideration of the parties' intent in its equitable allocation. See Kerr-McGee, 14 F.3d 321, 326 ("Although contractual arrangements between parties are not necessarily determinative of statutory liability, Lefton's intent to indemnify Kerr-McGee should be considered in the allocation of cleanup costs."). Moreover, to the extent that the court felt itself bound by the "polluter pays" principle or by our oblique reference to that principle in Beazer I, that conclusion was unwarranted. Because we conclude that the District Court's ultimate allocation of Beazer's costs was predicated in large part on this error, that conclusion was an abuse of discretion.

Mead would have us go further and prescribe that the purchase agreement factors must be prioritized on remand, but we think this is inappropriate. CERCLA places both the selection and weighing of equitable factors in the sound discretion of the district court, not the appellate court. Accordingly, we leave these matters for the District Court to decide on its own on remand, unfettered by the legal errors discussed above.

D. Any Declaratory Judgment Should Contain a Contingency Provision.

Finally, we are sympathetic with Mead's contention that the District Court's declaratory judgment fixing the parties' equitable shares of future response costs should contain a provision authorizing the parties to re-litigate the District Court's equitable allocation if new facts or future events render the current division inequitable. For example, Mead argues that once the investigatory phase of the case concludes and the remedial phase ensues, the District Court's equitable allocation would no longer be fair if any required remediation is "primarily or exclusively directed to those areas of the Site where Beazer is responsible for the majority of the contamination."

Because the equitable allocation proceeding in this case must be conducted again on remand by the District Court, the declaratory judgment already entered in this case is null and void. If and when the District Court enters a new declaratory judgment covering future costs, however, we agree with Mead that the judgment should contain some kind of provision authorizing the parties to re-litigate the allocation of those costs for good cause shown in response to new events or new evidence that would reasonably bear upon the equity of the allocation. Such contingency provisions are generally favored in CERCLA contribution actions, see United States v. Davis, 261 F.3d 1, 45 (1st Cir. 2001) (quoting contingency provision imposed by district court); Acushnet Co. v. Coaters, Inc., 972 F.Supp. 41, 69 (D.Mass. 1997); Boeing Co. v. Cascade Corp., 920 F.Supp. 1121, 1142 (D.Or. 1996), and we agree with the wisdom of those cases. We leave the specific design of the provision to the discretion of the District Court, with the help of the parties. We recognize Beazer's concern that Mead might use such a provision to re-litigate issues that will have already been decided in the equitable allocation proceeding to be conducted on remand, but we think this concern can be adequately addressed by application of the 'law of the case' doctrine.

VI. Conclusion

For the reasons stated above, we will reverse the judgments of the District Court and remand this action for further proceedings consistent with this opinion.