DIANE P. WOOD, Circuit Judge.

Lee Hatcher filed a civil rights suit under 42 U.S.C. § 1983 against the City of Indianapolis and several individually named defendants (collectively the City) challenging his seizure and a search of his dwelling and seeking $1 million in damages. After a trial, the jury awarded him $18,908.50. Hatcher appealed to this court, and the case settled for $100,000 plus attorneys' fees while the appeal was pending. The district court then, under rather unusual circumstances, awarded Hatcher a fraction of the attorneys' fees he sought. He appeals, and the City cross-appeals the court's decision to grant certain costs to Hatcher. We vacate and remand for further proceedings.

I

Hatcher's home was searched by a SWAT team on May 29, 1996. No narcotics were found, but he was arrested and brought to the Marion County jail on various drug charges. Those charges were later dismissed. Hatcher then filed this § 1983 suit against Steven Staal and two other officers involved in the raid; he brought a supplemental state law claim against the City. At trial, the jury found for Staal on the excessive force claim, but it found for Hatcher on his unlawful search and seizure claim and on his state law claim and awarded him $18,908.50 in damages. The parties cross-appealed the judgments, and the appeals were consolidated and submitted to this court's Settlement Conference Office. The parties then entered into a settlement providing for a $100,000 payment to Hatcher and his attorneys, which the parties agreed "resolve[d] all the issues raised by this lawsuit with the exception of legal fees claimed by [various lawyers]. . . ." Settlement Agreement, ¶ 2. The legal fees issue, according to the agreement, would "be referred to Magistrate V. Sue Shields for mediation and resolution." Id.

The district court was advised of the decision of the parties and seemed to endorse the referral to a named magistrate judge, although the parties never formally filed any other document in the district court indicating their consent to the referral. In accordance with the agreement, Magistrate Judge Shields set a briefing schedule and ordered a settlement/status conference to take place on September 25, 2001. At that point, without any prior announcement and for unexplained reasons, the district court decided to rule on the fee petitions itself. Those petitions were available to the court, because they had been filed in the district court prior to the time when the parties signed the Settlement Agreement. The court's order awarded attorneys' fees to Hatcher, but it reduced the requested amount of those fees by 70%, from $291,358.75 to $87,407.62. It also granted Hatcher's request for costs in the amount of $18,707.31.

II

The City's cross-appeal concerns only the grant of costs to Hatcher. It relies on the language in the Settlement Agreement quoted above, to the effect that the $100,000 payment covers everything except legal fees; the implication of that passage, according to the City, is that Hatcher's costs were included within the $100,000 payment. Hatcher's appeal asserts that the district court erred in two principal respects. First, he contends that the district court should not have ruled on the fee petitions at all but instead was obligated by the Settlement Agreement to abide by whatever Magistrate Judge Shields decided. Second, he argues that the district court abused its discretion by reducing his request categorically by 70% rather than applying the lodestar calculation to determine the reasonableness of the services and hours itemized by his attorneys.

Although we have serious doubts about the correctness of the analysis the district court used to evaluate the degree of Hatcher's success, because it erroneously used the jury's award of $18,908.50 as the benchmark instead of the $100,000 Hatcher received under the Settlement Agreement, we need not delve too deeply into the merits of the actual award. We agree with Hatcher that the district court never should have ruled on the fee petitions in the first place. What should have happened instead, however, is a more complicated question.

We enforce the terms of settlement agreements like those of any other contract, even when the agreement in question somehow limits the discretion of the courts. Dutchak v. Central States, Southeast Southwest Areas Pension Fund, 932 F.2d 591, 595-96 (7th Cir. 1991). The City, however, argues that this particular agreement cannot be enforced because it has never formally consented to the referral to a magistrate judge. Magistrate judges are judicial officers of the United States. As such, they are subject to the Code of Conduct for United States Judges, see Introduction to Code of Conduct, and they are subject to the same strict rules with respect to extra-judicial activities and sources of income as are all other judicial officers appointed under either Article III or Article I of the Constitution. See Code of Conduct for United States Judges, Canons 5 and 6. The authority of magistrate judges is regulated by 28 U.S.C. §§ 631-39. The City is particularly concerned with the provision in 28 U.S.C. § 636(c), which permits a magistrate judge to make dispositive orders in a civil case only when the parties have given their written consent to this manner of proceeding.

The City is splitting hairs here. There is nothing wrong with the procedure the parties used to indicate their consent, although there is a more difficult question about the content of that consent, to which we turn in a moment. The City is correct that § 636(c) requires the consent of the parties for a magistrate judge to assume full responsibility for a case. This consent must be "clear and unambiguous . . . [it] must be explicit and cannot be inferred from the conduct of the parties." Jaliwala v. United States, 945 F.2d 221, 224 (7th Cir. 1991) (quotation marks and emphasis omitted). But we have all of that. The parties signed a written document in which they agreed that the attorneys' fee issue will be "resolved" by Magistrate Judge Shields. This easily serves as a reference to the magistrate judge. See Rice v. Sunrise Express, Inc., 209 F.3d 1008, 1013 n. 7 (7th Cir. 2000) (consent need not take a particular form, so long as it is explicit and on the record). There is nothing in § 636(c) requiring that any specific form be filled out, nor have we found such a requirement in the local rules. The word "resolve" can only be interpreted as a consent to the entry of a judgment dealing with the disputed issues.

Under the statute and the local rules in force in the Southern District of Indiana, there is no need for case-by-case approval of a reference to a magistrate judge. Nevertheless, in this case the district court acknowledged that the reference was being made when he told the parties that he would give Magistrate Judge Shields a "heads up" on the matter. Once a civil case is referred to a magistrate judge, that reference may be withdrawn only if the district court, on its own motion, finds good cause to do so, or if any party shows that extraordinary circumstances have arisen that require this step. See 28 U.S.C. § 636(c)(4); see also Dixon v. Ylst, 990 F.2d 478, 480 (9th Cir. 1993). In this case, neither one of those events justifying withdrawal occurred: the district court made no finding that good cause existed before it de facto withdrew the case by entering its own order on the merits, nor did any party request withdrawal of the reference. Moreover, the court gave the parties no notice that the procedure to which they had agreed was being set aside. To the extent the parties were invoking magistrate judge authority through their settlement agreement, they were entitled to follow that procedure. Before reasserting control over the case, the district court should have followed the procedures of § 636(c)(4); had it done so, it is quite possible that it would have noticed the more serious problem with this case.

That problem has to do with the difference between consenting to referral of a case to "a" magistrate judge, as opposed to consenting only to referral to a specific named magistrate judge whom the parties have hand-picked. The Settlement Agreement purported to choose one particular magistrate judge from among those serving in the Southern District of Indiana. As the district court docket sheet reflects, Magistrate Judge Shields was not the original magistrate judge assigned to this case through the district court's routine assignment procedures. When asked about the referral to a specific magistrate judge at oral arguments, Hatcher's lawyer freely admitted that the parties chose Magistrate Judge Shields because "both parties knew her and recognized her as to be a competent person to resolve it [the dispute] and that was the purpose behind" choosing her. Hatcher insists that this court has approved of such a procedure in the past, but a closer look at the cases on which he relies shows that we have done no such thing. As we make clear in this opinion, the degree of specificity the parties sought in this case is inconsistent with the role of magistrate judges as federal judicial officers. In general, of course, parties are not permitted to select their own judges in cases in federal court. See 28 U.S.C. § 137 (providing that the rules and orders of a court with more than one judge shall provide for the division of business among district judges). The parties in this appeal had to take the panel the Seventh Circuit's procedures served up to them, just as they were obliged to accept the district court's assignment of a particular district judge. We must decide whether there is something so different about magistrate judges that parties can limit their consent under 28 U.S.C. § 636(c) in a manner that disregards the assignment procedures otherwise used in that district court for allocating work to the magistrate judges.

Hatcher suggests that there is nothing wrong with the procedure followed here, relying in part on Tyson v. Trigg, 50 F.3d 436, 439-42 (7th Cir. 1995). In that case, we held that a state defendant's due process rights were not violated when a prosecutor's knowledge of local procedures had the effect of enabling him indirectly to select the judge who would preside over a rape prosecution. This ability on the prosecutor's part stemmed from the way the grand juries operated. Each of the six grand juries to which a proposed indictment might be presented was assigned to a specific judge. By selecting a specific grand jury, the prosecutor was effectively able to choose the judge to whom the case would eventually be assigned. Id. at 439. The question before us was whether the defendant's rights were violated by this procedure. The answer there was no, but this does not establish the converse proposition, namely, that one's rights are violated when one cannot choose a judge. Furthermore, Tyson was concerned with whether a state law violated the federal constitution, while we are concerned here with the proper administration of the federal judiciary.

The best support we can find for the arrangement the parties adopted here comes from a recent case in our court that held — under the circumstances of that case — that consent to one particular magistrate judge did not imply that the parties had consented to a different magistrate judge. Kalan v. City of St. Francis, 274 F.3d 1150 (7th Cir. 2001). See also Mendes Junior Int'l Co. v. M/V Sokai Maru, 978 F.2d 920, 924 (5th Cir. 1992) (finding that consent to have case heard by one magistrate judge, coupled with a judicial order designating that judge to hear the case, did not confer authority on a different magistrate judge when no additional consent or judicial designation transferring the case to the new judge existed). Kalan contains language that Hatcher interprets as endorsing the proposition that parties can broadly specify the particular magistrate judge they wish to use in any case. He argues further that Kalan implicitly rejects the argument that § 636(c) does not and cannot confer such a power on the parties for use in a public court system. 274 F.3d at 1153.

Kalan involved an appeal from a denial of a motion for relief under FED. R. CIV. P. 60(b). The panel, which decided the case per curiam, did not reach the merits because it believed that flaws in the consent procedure for the magistrate judge required it to dismiss for want of jurisdiction. Thus, the narrow holding of the case was only that a consent may be ineffective if a judge other than the one who was named consistently with the court's procedures is assigned to the case. Hatcher infers from this rule that parties always have the right to limit a consent to a particular individual, but we do not read it that broadly.

Close attention to the facts and holding in Kalan show that this court enforced the parties' agreement only insofar as it depended upon the facts that existed at the time of the agreement. Unlike the parties in our case, the parties in Kalan did not themselves pick the magistrate judge who was to handle their case. Instead, knowing which magistrate judge was assigned to their case through the district court's routine assignment procedures, they consented to the referral of the case to that individual. In our case the parties attempted to override the district court's assignment protocol and to substitute their own chosen magistrate judge. That presents an entirely different situation, and one that we cannot endorse. It is one thing for parties, knowing in advance to whom their case will be referred, to limit consent to that particular referral, and it is another thing to allow them to shop among a district court's magistrate judges. Kalan acknowledges that the former may occur under the procedures used in some districts, and it holds that this does not violate any rule. The latter, however, presents more fundamental problems.

Simply put, we see no distinction between the position of the magistrate judges for this purpose and the position of any other judicial officers exercising power in the federal courts. As we noted before, no one would think of arguing that parties had the right to select a particular district judge or panel of the court of appeals. Parties who do not like the judge they are given must satisfy the stringent requirements of 28 U.S.C. §§ 144 or 455 before they are entitled to have a different judge assigned to their case. It is telling in this context that § 455(a) specifically refers to "[a]ny justice, judge, or magistrate judge of the United States," in describing the officers to whom its provisions apply. Other clues in the statutes also indicate that magistrate judge assignment is a matter for the court to decide, not the parties. Nowhere does § 636 provide for the parties' choice of a specific magistrate judge: "Upon the consent of the parties, a full-time United States magistrate judge . . . may conduct any or all proceedings." § 636(c)(1) (emphasis added). The magistrate judge may do so only "when specially designated to exercise such jurisdiction by the district court or courts he serves." Id. This can mean only that it is the court, and not the parties, that has the power to confer general or specific duties upon an individual magistrate judge. Cf. DDI Seamless Cylinder Int'l, Inc. v. General Fire Extinguisher Corp., 14 F.3d 1163, 1166 (7th Cir. 1994) (holding that the parties could not designate a magistrate judge as an arbitrator). This court has taken the view that two prerequisites exist for a valid reference to a magistrate judge: (1) consent of the parties and (2) special designation by the court. Sunrise Express, Inc., 209 F.3d at 1014 n. 7. Nothing in that system explicitly supports the idea that the parties may commandeer this entire process in lieu of the court.

Kalan took a slightly different tack. It started off from the premise that nothing in § 636(c)(1) prevents the parties from agreeing to a referral to a magistrate judge, knowing in advance which person would be assigned to their case. It then added that the consent itself had to be understood in light of this pre-existing situation. We have no quarrel with Kalan, to the extent that it reflects only the real-world fact that parties may be influenced in their decision whether or not to consent to magistrate judge jurisdiction by the knowledge of which individual will acquire responsibility for their case. Nevertheless, we think that it would be an inappropriate extension of Kalan and a construction of § 636(c)(1) that the statute simply will not bear to allow parties to designate a magistrate judge independently of the district court's procedures for magistrate assignment. The language in the statute that indicates that the magistrate judge may exercise her power "when specially designated to exercise such jurisdiction by the district court or courts" is inconsistent with a rule permitting the parties effectively to make that designation.

Moreover, as we have already noted, the other background rules governing magistrate judges, including ethical rules about the activities in which they may engage and the disqualification rules, put them on a par with Article III judges when they are exercising judicial power. An important way in which the federal courts strive to fulfill their role as the impartial and apolitical "third branch" of government is their insistence on equal respect for, and responsibility of, each individual judge. (We are not unaware that parties may engage in different procedural stratagems designed to make their case wind up in front of a preferred judge, but acknowledgment that these kinds of judge-shopping efforts exist is quite a different thing from outright endorsement of them.) In our view, the general rule that one may not choose one's judge in federal court should not have an exception for magistrate judges. Once a party has submitted a justiciable dispute to a federal tribunal, it is up to the court to designate the judge. If the parties here had preferred a system under which they could name the individual who would resolve the legal fees issue, nothing would have prevented them from entering into a binding arbitration agreement to that effect. But that is not what they did, and we think their decision to use the courts carried with it a certain loss of discretion over the identity of the judicial officer who would preside.

As a last observation on this topic, we note that the Local Rules of the U.S. District Court for the Southern District of Indiana provide that selections of magistrate judges are to be made at random. See Local Rule 72.1(h) ("Upon the consent of the parties, a full-time Magistrate Judge is hereby authorized and specially designated to conduct any or all proceedings in any civil case which is filed in this Court.") (emphasis added). District courts are entitled to enact such rules, which relate to the administration of the court's business. See FED. R. CIV. P. 83(a); In re Establishment Inspection of Gilbert Bennett Mfg. Co., 589 F.2d 1335, 1340 (7th Cir. 1979) (district court may pass local rules regarding magistrate judges to aid it in the performance of its business); see also United States v. Claros, 17 F.3d 1041, 1044-45 (7th Cir. 1994) (promulgation of local rules permissible as long as the rules are not "inconsistent with the Constitution, a statute of the United States, or with a national rule governing the conduct of litigation in the United States courts").

The remaining question is the proper disposition of this appeal, given our conclusion that the selection of a particular magistrate judge here was impermissible. Three options are available: (1) we could simply decide, as the City urges, that there was no effective consent and evaluate the merits of the district court's decision on fees, (2) we could rule that the consent to Magistrate Judge Shields was an effective consent to any and all magistrate judges in the district, or (3) we could remand this case for further proceedings. Because the rule we are announcing today may not have been clear in light of the different possible interpretations of Kalan, we think it best under all the circumstances to remand the case to the district court for further proceedings. The parties consented to something, and we have rejected the City's formalistic argument about the writing in which that consent was embodied. This leaves us with an ambiguity in the Settlement Agreement that must be resolved by reference to extrinsic evidence or by further agreement of the parties. See, e.g., Air Line Stewards Stewardesses Assoc. v. American Airlines, Inc., 763 F.2d 875, 878 n. 3 (7th Cir. 1985). If on remand the district court concludes that the parties meant to refer the dispute to any magistrate judge designated in accordance with the court's normal rules, it should carry out the terms of their consent accordingly. If it concludes that the parties meant to select only Magistrate Judge Shields, then the reference cannot be carried out and the consent is ineffective. In the latter instance, the case will remain with the district court unless the parties execute a new consent, and the court must reconsider its award of fees and costs, using the $100,000 figure as the amount Hatcher gained in this litigation.

III

The judgment of the district court is VACATED and the case is REMANDED for further proceedings consistent with this opinion.