CALABRESI, Circuit Judge:

This appeal, brought by various current, former, and retired sales agents of the Knights of Columbus, concerns a challenge to the Knights' Pension Plan. Under the Knights' plan, retirees receive a fixed pension benefit, but the amount is reduced by, among other things, any renewal commissions payable to the agent. Renewal commissions are benefits that a sales agent receives after having been with the Knights for five years. See Bonovich v. Knights of Columbus, 963 F. Supp. 143, 147 (D. Conn. 1997). If a policy initially sold by an agent gets renewed, then that agent receives an annual "renewal commission" from that policy, for up to a maximum of five years from the policy's initial sale. The renewal benefits are paid whether the agent remains with the Knights or has retired or left for any other reason.

The practice that the Knights' pension plan has adopted, with respect to renewal commissions, is a form of pension integration. "Integration" occurs when a collateral source of income is folded into a retiree's pension benefits, so that the pension plan's obligation is reduced while the retiree maintains a constant level of income. In other words, integration is a form of set-off: if an employee received a fixed payment per month, but then begins to receive additional payments from another source deemed appropriate, e.g., Social Security, a plan that "integrates" such benefits will reduce the amount payable by the plan, dollar-for-dollar, in response to the new source of income. The effect is that the retiree's income remains constant, but the pension plan pays a smaller portion of the total.

The plaintiffs in this appeal sought to initiate a class action to attack the integration of renewal commissions contained in the Knights' pension plan. They contend first that this integration violates the nonforfeitability clause of the Employee Retirement Income Security Act ("ERISA"), by divesting them of the portion of their entitled benefits that is offset by their renewal commissions. See 29 U.S.C. § 1053(a) ("Each pension plan shall provide that an employee's right to his normal retirement benefit is nonforfeitable upon the attainment of a normal retirement age."). Defendants answer that the offset of renewal commissions is nothing more than a part of the calculation algorithm that defines the ultimate pension benefits receivable. As such, they claim, the integration reflects a permissible agreement by the parties who negotiated and defined the pension plan. See 29 U.S.C. § 1002(19), interpreted in Nachman Corp. v. Pension Benefit Guaranty Corp., 446 U.S. 359, 372-73 (1980). Plaintiffs respond that even if this were so (which they forcefully deny), the Knights' plan is supposedly noncontributory. Instead, by offsetting the renewal commissions the Knights force pensioners to fund a portion of their retirement benefits — at least for up to the first five years of retirement — with these commissions. For this reason, plaintiffs have not only brought this action under the nonforfeiture clause of ERISA, but also under the doctrine of equitable estoppel (to prevent the Knights from rendering their putatively noncontributory plan contributory).

The United States District Court for the District of Connecticut (Janet Bond Arterton, Judge), in a comprehensive published opinion, rejected both contentions, and granted defendants' motion to dismiss the plaintiffs' suit. See Bonovich, 963 F. Supp. at 144-49.

On the forfeiture issue, the parties base their arguments on their respective readings of the Supreme Court's opinion in Alessi v. Raybestos-Manhattan, Inc., 451 U.S. 504 (1981). The estoppel question depends, instead, on the meaning and applicability of several courts of appeals' decisions. We begin by examining Alessi and ERISA, and then turn to estoppel.

I. FORFEITURE A.

In Alessi, a group of retirees launched a global attack on the practice of integration, claiming that any integration violated the nonforfeiture clause of ERISA. But, as the Supreme Court pointed out, ERISA expressly provided for the integration of Social Security and Railroad Retirement benefits. See id. at 513 (citing 29 U.S.C. §§ 1054(b)(1)(B)(iv), (C), (G)). Accordingly, the Alessi retirees' argument is best recast as claiming that only Social Security and Railroad Retirement may be integrated, and that all other forms of integration are impermissible. Consistent with their position, the Alessi retirees also challenged, as violating the nonforfeiture clause, a regulation of the Treasury Department that permitted integration for a broader array of benefits, including those at issue in the Alessi case, workers' compensation payments. See 26 CFR § 1.411(a)-4(a).

The Supreme Court rejected the retirees' arguments. It concluded that integration does not necessarily violate ERISA. The High Court then both upheld the plan before it and refused to strike down the Treasury Regulation under attack. Of this much there is no doubt. What else Alessi did is, however, far from clear. And the lower courts have differed widely in their readings of the case and its scope. (See Judge Cudahy's insightful opinion in Huppeler v. Oscar Meyer Foods Corp., 32 F.3d 245 (7th Cir. 1994), which outlines numerous interpretive difficulties with the Alessi opinion and analyzes the responses of various courts to Alessi.)

The key point of contention has been the degree to which Alessi condones the practice of integration under ERISA. Some courts believe that Alessi should be read as a blanket endorsement of any form of integration, see, e.g., PPG Indus. Pension Plan A v. Crews, 902 F.2d 1148, 1150-51 (4th Cir. 1990). Others, instead, argue that the Supreme Court in Alessi only permitted integration of certain types of benefits, those that "match up" or share a nexus of some sort with the pension plan. See, e.g., Employee Benefits Comm. of the Retirement Sys. of Hawaiian Tel. Co. v. Pascoe, 679 F.2d 1319, 1321-22 (9th Cir. 1982). In the instant appeal, plaintiffs contend that the integration of the renewal commissions in the Knights' plan is exactly the sort of integration that the Supreme Court would not have allowed. For their part, defendants adhere to the view that all integration is permitted, and therefore that their plan necessarily presents no affront to ERISA.

Courts that believe that the Supreme Court meant to cabin — at least to some extent — the practice of integration have tended to rely on Alessi's discussion of certain revenue rulings issued by the IRS. These revenue rulings — some of which pre-dated the enactment of ERISA — did not deal with ERISA forfeiture at all, but concerned the interaction between integration and the antidiscrimination provisions of the Tax Code. Nevertheless, in speaking of some of these IRS rulings, the Supreme Court observed that:

[they] base their allowance of pension payment integration on three factors: the employer must contribute to the other benefit funds, these other funds must be designed for general public use, and the benefits they supply must correspond to benefits available under the pension plan. The IRS employed these considerations in approving integration with workers' compensation benefits. E.g., Rev. Rul. 69-421, Part 4(j), 1969-2 Cu. Bull. 72; Rev. Rul. 68-243, 1968-1 Cu. Bull. 157.

Alessi, 451 U.S. at 520 (emphasis added).

By focusing on the third requirement of the revenue rulings cited in Alessi, the courts that have upheld only some forms of integration have crafted a "nexus" test to determine whether or not benefits may be integrated. Such a test requires that the integrated income stream's payments bear some correlative relationship to the income-replacement function of pensions. Thus the Ninth Circuit, a leading nexus court, has ruled that Alessi forbids the integration of workers' compensation payments that relate to restitution for bodily injury, because such benefit payments have no connection to the wage-replacing purpose of pensions. See Pascoe, 679 F.2d at 1321-22.

Other courts have, instead, centered their attention on the parts of Alessi that focus on the parties' freedom to establish, by contract, whatever plan they wish to create, see Alessi, 451 U.S. at 511-12. As a result, these courts have read no such nexus requirement into either Alessi or ERISA. See, e.g., PPG Indus., 902 F.2d at 1150 (without any discussion of the revenue rulings, interpreting Alessi to permit all forms of integration).

Our own circuit has expressly declined to weigh in. See Reska v. Pension Plan of Bethlehem Steel Corp., 848 F.2d 372, 375 (2d Cir. 1988).

B.

Plaintiffs, in challenging the Knights' integration practice, hone in on the revenue rulings discussed by the Supreme Court. They argue, relying on those circuits that have read the nexus requirement into the Alessi opinion, that the Supreme Court "adopted" the revenue rulings into the ERISA statute. And they contend that because the Knights' provisions would fail at least some of the requirements of these rulings, the Knights' integration of renewal commissions (unlike the integration of the workers' compensation benefits at issue in Alessi) violates ERISA. Defendants, relying on the cases that have totally rejected the nexus requirement, respond that Alessi's citation of the revenue rulings was no more than a passing reference, and that the Alessi Court in no way meant to make compliance with these revenue rulings a prerequisite for integration. They contend, instead, that the essence of Alessi is to be found in the parts of the opinion that focus on the parties' contractual freedom to establish whatever retirement plans suit them.

Although we think defendant's characterization of the revenue rulings is the more accurate of the two, we need not (and hence do not) read Alessi as going so far in the contractual freedom direction as defendants urge. As an initial matter, we believe that the defendants are correct in concluding that the Court's discussion of the revenue rulings was unnecessary to its resolution of Alessi. Accordingly, we reject plaintiffs' argument that the alleged failure of the Knights' plan to meet the IRS's three-part test precludes comportment with ERISA. And we hold that no such test is required by Alessi. In this regard, we are apparently in agreement with the Seventh Circuit. See Huppeler, 32 F.3d at 251.

We note, however, that dismissal of the significance of the revenue rulings does not conclude the nexus debate. In this regard, we evidently disagree with the Seventh Circuit. See Huppeler, 32 F.3d at 251-53. And we reject the proposition that the nexus requirement stands or falls with the "status" of the Supreme Court's discussion of the revenue rulings. Indeed, we believe that the notion of "nexus," as a general concept that may limit the degree of permissible integration in ERISA plans, is one that can be culled from various parts of the Supreme Court's opinion in Alessi. See, e.g., Alessi, 451 U.S. at 520-21 n.16 (discussing other revenue rulings and analyzing general themes). Because the Knights' plan satisfies whatever nexus test Alessi might impose, however, we need not resolve whether Alessi — or ERISA itself — creates such a requirement. Accordingly, we adhere to our prior refusal to decide the question. See Reska, 848 F.2d at 375.

C.

The renewal commissions provided by the Knights' plan are not readily comparable to other benefits, such as restitution for bodily impairment, whose integration have been successfully attacked as inconsistent with ERISA. See, e.g., Pascoe, 679 F.2d at 1322-23. They share, moreover, various attributes with those benefits that have been deemed integratable. See, e.g., Pritchard v. Rainfair, Inc., 945 F.2d 185, 187-190 (7th Cir. 1991) (upholding the integration of the company's private profit-sharing plan payments into the retirement pension); Vintilla v. United States Steel Corp. Plan for Employee Pension Benefits, 606 F. Supp. 640, 643 (W.D. Pa.) (upholding pension plan's integration of severance payments), aff'd 782 F.2d 1033 (3d Cir. 1988) (unpublished table decision).

Like the plans that have been upheld, the private payments before us confer pecuniary benefits that serve the basic function of pensions, namely, to take the place of wages for retirees. That is the heart of the nexus "requirement." They do not arise independently of the employment relationship. They are not, that is, like lottery winnings by the pensioner, integration of which would constitute a windfall for the employer. Nor do they constitute reimbursements for special expenses or burdens that have fallen on the retiree. They are not, that is, like compensation payments for physical injuries or pain and suffering, which, if integrated, would undercut the wage replacement function of the pension plan.

Finally, the renewal commissions cannot be construed as being previously earned and vested deferred wages, whose payment is being spread out over five years. In this respect, it is critical that the benefits are private, discretionary, indefinite in amount, and that — in a significant sense — it was up to the employer and employees to define their scope in contractual negotiations. Thus, had the parties been so inclined, they could have made the renewal commission a bonus that was limited to those agents who had been with the Knights for five years and who remained in active service with the Knights. The fact that, instead, they chose to define the renewal commissions as available to all five-year agents, including those in retirement, but then to restrict the total retirement benefits (by integrating these commissions into the pension plan) in no way raises the spectre of "forfeiture."

Under the circumstances, and because of their wage-related nature (and wage-replacing function for retirees), we find that the renewal commissions satisfy whatever nexus requirement Alessi could be read to mandate. And we decline to answer the question we left open in Reska: does ERISA permit the integration of payments into a pension plan in the absence of a nexus between those payments and that plan?

II. ESTOPPEL

We therefore turn to the issue of the proper application of the equitable estoppel doctrine to ERISA cases. Specifically, we must consider plaintiffs' contention that since the Knights describe their pension plan as "noncontributory," they are estopped from defending the integration of the agents' renewal commissions into the plan.

The district court conducted an analysis under Schonholz v. Long Island Jewish Medical Center, 87 F.3d 72, 78-80 (2d Cir.), cert. denied, 117 S.Ct. 511 (1996), and Lee v. Burkhart, 991 F.2d 1004, 1009 (2d Cir. 1993), and found that dismissal of plaintiffs' estoppel claim was warranted. It correctly stated that:

The Second Circuit has held that the principles of estoppel apply in ERISA cases only under extraordinary circumstances. Schonholz v. Long Island Jewish Medical Center, 87 F.3d 72, 78 (2d Cir. 1996); Lee v. Burkhart, 991 F.2d 1004, 1009 (2d Cir. 1993). The elements of a promissory estoppel claim in an ERISA action are: (1) a promise, (2) reliance on the promise, (3) injury caused by the reliance, and (4) an injustice if the promise is not enforced. Schonholz, 87 F.3d at 79. Further, for purposes of ERISA, a plaintiff must demonstrate a promise that the defendant reasonably should have expected to induce action or forbearance on the plaintiff's part. Id.

Bonovich, 963 F. Supp. at 148.

The district court concluded that the plaintiffs had not met these requirements. On appeal, the defendants argue that the district court should not even have initiated an estoppel analysis because the lack of a facial ambiguity in the terms of the pension plan imposes a threshold bar on a plaintiff seeking to bring an estoppel claim. This argument finds its roots in Kane v. Aetna Life Insurance, 893 F.2d 1283, 1285-86 (11th Cir. 1990). Kane reasoned that a promise that relates to an ambiguous plan may be construed as a permissible "interpretation" of that plan, but that a promise that relates to an unambiguous plan is effectively a "modification" of that plan. As such, the latter type of promise is not governed by the federal common law doctrine of estoppel, but must instead satisfy the statutory requirements that regulate pension plan modifications. And the statute — at least as construed by the Eleventh Circuit — dictates that any modification must be in writing. See Nachwalter v. Christie, 805 F.2d 956, 960 (11th Cir. 1986) (interpreting 29 U.S.C. § 1102(a)(1)).

The Kane rule is not the law in this circuit. See Cerasoli v. Xomed, Inc., 972 F. Supp. 175, 180 (W.D.N.Y. 1997) ("The Second Circuit has not addressed this issue [of the Kane rule], and if the facts before us are as alleged in the complaint, this case might illustrate why such a rule would be undesirable."). Nor do we see any reason to adopt Kane at this time. The district court's rejection of plaintiffs' estoppel argument was correct and was properly grounded in this circuit's precedents — Schonholz and Lee. Accordingly, we affirm both its reasoning and its result.

III. CONCLUSION

Because of the confusion that pervades this area of the law — a field that hungers for clarification from higher sources — we will summarize what we have held. First, we reiterate that the Supreme Court in Alessi did nothing more than reject the argument that Social Security and Railroad Retirement benefits were the only income streams integratable under ERISA. And, in so doing, it understandably upheld a challenged Treasury Department Regulation that was consistent with its basic holding. Second, we conclude that the Alessi Court's discussion of certain IRS revenue rulings was not meant to deem compliance with those rulings (or with their supposed three-part test) as the determinant of whether benefits may be integrated under ERISA. Third, we caution that our holding does not construe Alessi as foreclosing a "nexus" requirement in assessing the legality of the integration of independent sources of income into pension plans. As we have held before, that is an open question in our circuit. See Reska, 848 F.2d at 375. Fourth, we hold that the integration of privately defined, wage-related pecuniary benefits, such as the renewal commissions in this case, sufficiently satisfies whatever nexus requirement Alessi might impose. Finally, we confirm that estoppel actions arising under ERISA are properly conducted, in our circuit, under the rules of Schonholz and Lee. With these clarifications, and in remaining part for the reasons articulated in Judge Arterton's comprehensive opinion, see Bonovich, 963 F. Supp. 143, we order that the judgment of the district court be

AFFIRMED.