The Central States, Southeast and Southwest Areas Pension Fund (Central States) is a well known multiemployer pension plan that serves members of the International Brotherhood of Teamsters who work in the midwestern United States. For years, Safeway operated many grocery stores in Central States' coverage area. The employees in these stores were covered by collective bargaining agreements with the Teamsters. As part of those arrangements, Safeway was required to make contributions to the plan for more than 1500 employees. In the late 1980s, Safeway sold the divisions that employed most of the plan members. By 1989, Safeway owned only one store that employed plan participants. This was its Eau Claire, Wisconsin, store, where 16 plan members worked. This case concerns the payments Safeway must make to Central States as a result of these changes in its business--changes known as "partial withdrawals" from the pension fund. The district court concluded that Safeway owed approximately $1.9 million for a 1993 partial withdrawal assessment. We affirm.

* Employers who are part of multiemployer plans make contributions on the basis of the number of their employees covered by the plan (who are converted into the antiseptic-sounding "contribution base units"). So, if an employer's workforce shrinks or the employer goes out of business, that employer reduces or ends its contributions to the plan. This could cause problems, because plan participants continue to enjoy their right to benefits upon retirement. If employers could simply stop contributing when they go out of business, downsize, or, as in this case, sell the divisions employing plan participants to somebody else, a plan could find itself substantially underfunded. To deal with this problem, Congress enacted the Multiemployer Pension Plan Amendments Act of 1980 (MPPAA), Pub. L. No. 96-364, 94 Stat. 1208 (codified in scattered sections of 29 U.S.C.). The MPPAA creates "withdrawal liability" for employers that leave plans. Basically, when an employer pulls out, the plan in which it participated is permitted to approximate the degree to which it is underfunded (its "unfunded vested benefits," or UVBs), and then charge the employer for its share of those UVBs. Moreover, under 29 U.S.C. sec. 1385, employers are subject to partial withdrawal liability when their contributions decline substantially over a period of several years. This is what happened to Safeway.

Under the rules for determining when a partial withdrawal occurs, Safeway first incurred withdrawal liability in 1990 for its 1987 and 1988 asset divestitures. Central States demanded $16.3 million from Safeway; eventually, they settled on $12.6 million. This settlement was confirmed in November 1993. In 1995, Central States came calling again, this time claiming that Safeway incurred partial withdrawal liability for 1993. The gross assessment was $11,299,544, but Safeway received a credit for its 1990 payment, making the net demand $1,985,363. Despite the hefty reduction that took into account the earlier payment, Safeway argued that it was entitled to an even greater credit. Central States disagreed, relying on the credit rules that are contained in the regulations issued by the body responsible for overseeing Employee Retirement Income Security Act (ERISA) plans, the Pension Benefit Guarantee Corporation (PBGC). Safeway responded that those regulations are unreasonable since their use resulted in a nearly two million dollar assessment even though no additional assets were sold. Its 1993 liability rested instead only on the statutory definition of a "partial withdrawal."

Anticipating that plans and employers will occasionally have disputes over the applicability of the rules, the MPPAA creates a "pay first, fight later" regime under which a dispute over withdrawal liability is referred to arbitration, but only after the employer turns the disputed amount over to the plan. See 29 U.S.C. sec. 1401(d). This is the path Safeway followed. It initiated an arbitration proceeding to contest the fund's calculation of its 1993 withdrawal liability and the credit method the fund used. In an interim decision, the arbitrator first decided that the settlement agreement with respect to the 1990 withdrawal assessment (which led to the $12.6 million figure mentioned above) did not operate as a bar of the 1993 partial withdrawal demand. Second, the interim decision held that the fund was not estopped from applying its credit method because it had not specifically notified Safeway that it was going to change its practice. The change arose from a final credit regulation published in the Federal Register, 57 Fed. Reg. 59,808 (Dec. 16, 1992), which was notice to the world that the fund would be required to change its method. Last, the arbitrator decided that the fund's calculation of Safeway's 1993 withdrawal liability was flawed. The fund used what is called the "modified presumptive method" of calculating withdrawal liability established in ERISA sec. 4211(c)(2). But it applied a 10-year allocation period, found in a separate subsection of ERISA, sec. 4211(c)(5)(C). The arbitrator found that the fund could not put these together and thus could not use a 10-year allocation period consistently with ERISA sec. 4206 and the applicable credit regulations. Instead, it had to use the five-year period found in credit regulation 29 C.F.R. sec. 2649.4. In accordance with the arbitrator's ruling, Central States recalculated Safeway's withdrawal liability using the five-year allocation period, but that led it to revise its 1993 demand upward, to approximately $2.2 million. In his final decision, the arbitrator essentially threw up his hands in dismay. He expressed the opinion that he was "convinced that the Fund is due additional payment because of the 1993 partial withdrawal and that the Employer is entitled to a reasonable credit for the payment that it made because of the prior withdrawal." But he ultimately concluded that the regulations were so irrational that they did not provide direction to the fund to calculate a proper credit and thus that its demand for payment had to be set aside.

Central States then appealed to the district court, as permitted by 29 U.S.C. sec. 1401(b). Safeway argued, as it had before, that the agreement that settled the 1990 dispute precluded Central States' request, that Central States was estopped from demanding money for the 1993 withdrawal by virtue of statements made by one of its representatives, and that the regulations providing for subsequent withdrawal liability were so incoherent as to be irrational and unenforceable. It also urged that the regulation was unconstitutional as applied to it, either as a taking or as a violation of substantive due process. The district court, properly reviewing the arbitrator's legal conclusions de novo, see, e.g., Joseph Schlitz Brewing Co. v. Milwaukee Brewery Workers' Pension Plan, 3 F.3d 994, 999 (7th Cir. 1994), affirmed on other grounds, 513 U.S. 414 (1995), disagreed with all of Safeway's arguments and vacated the arbitration award. It also concluded that the arbitrator had erred in finding that Central States could not use a 10- year allocation period for its 1993 demand. Consequently, the court held that Safeway was liable for the $1,985,363 originally demanded by Central States and that, since Safeway had paid up, Central States could simply keep the money and the case was closed. Safeway now appeals; Central States, having seen what the five-year period would do for it, has cross-appealed to argue that this is the one that should apply.

Before we can consider the district court's reasoning, we must address a jurisdictional argument that Central States has presented. It claims that the district court lacked jurisdiction over Safeway's request to enforce the arbitrator's award because it came too late. Under 29 U.S.C. sec. 1401(b)(2), a party has 30 days to bring an action in district court to "enforce, vacate, or modify" an MPPAA arbitration award. The arbitrator's final decision was dated March 21, 1998; Central States filed its action to vacate the award on April 1, 1998, but Safeway did not file its counterclaim until May 29, 1998, well more than 30 days beyond the arbitrator's decision. Central States seems to think that this leaves the arbitrator's award in some state of limbo, under which it is not enforceable, because no timely petition for enforcement was filed. It follows, according to Central States, that it can keep the money. This, we think, is a real stretch at best, and at worst a serious misunderstanding of the position in which the party who is content with an arbitral award finds itself. But there are other reasons as well for rejecting Central States' argument.

Central States' position is premised on two points: first, that the 30-day period provided by sec. 1401(b)(2) applies here, not the six-year limitations period for ERISA actions contained in 29 U.S.C. sec. 1451(f) (or the three-year period that applies when the plaintiff knows or should know of the cause of action), and second, that the 30 days given by sec. 1401(b)(2) are jurisdictional in the strong sense of the term-- that is, nonwaivable and not subject to doctrines like estoppel. The district court, relying on the reasoning of the Third Circuit in Trustees of Amalgamated Ins. Fund v. Sheldon Hall Clothing, Inc., 862 F.2d 1020 (3d Cir. 1988), found that sec. 1451(f) was the more apt statute and thus that its six-year period applied. Sheldon Hall Clothing found that although the 30-day limit should apply when a party wants to vacate or modify an award, it was not reasonable to impose a 30-day limit on an action to enforce the award. Consequently, it concluded that the more general six-year period applies to an action solely to enforce an arbitral award.

We are doubtful about this. The language of sec. 1401(b)(2) says that it applies to actions to "enforce, vacate, or modify"; the statute draws no distinction among these types of actions. Nor, as the parties' extensive argumentation in this case illustrates, is it easy to distinguish one type of action from another. Safeway claims that it merely wants the award enforced, while Central States says that Safeway really wants a modification. The Third Circuit in Sheldon Hall Clothing was concerned that the limitations period provided in sec. 1401(b)(2) might be too short, since a party may need more than 30 days to determine if the loser in arbitration is willing to comply with the terms of the award. Moreover, the Third Circuit thought that it made little sense to allow a party to escape an arbitration award merely by waiting 30 days and then ignoring the award with impunity. But this assumes that a party wishing to enforce an arbitration award under sec. 1401(b)(2) must wait until the losing party has violated the award in order to bring its action in the district court. This is not the way sec. 1401(b)(2) reads. Instead, it says that "any party [to the arbitration] may bring an action to enforce." The reference to "any party" (rather than, say, "any party aggrieved") undercuts the notion that only the loser in arbitration can bring an action. Nor does such a rule comport with practice. See, e.g., Central States, Southeast and Southwest Areas Pension Fund v. Paramount Liquor Co., 203 F.3d 442, 445 (7th Cir. 2000) (holding that suits brought by victorious employer and losing plan in separate venues were equally appropriate). Victorious in arbitration, Safeway could have then gone to court to reduce its arbitration award to a judgment pursuant to sec. 1401(b)(2).

We need not decide, however, if there are ever circumstances under which the longer statute might apply. There can be no doubt that an action is proper within 30 days, and if there are ways of extending that period, the action would also satisfy the 30-day rule. The question thus is whether the 30-day period has any flexibility, or if it is rigidly jurisdictional such that the district court has no power over the case if the appeal is filed too late. We stated in Central States, Southeast and Southwest Areas Pension Fund v. Navco, 3 F.3d 167, 173 (7th Cir. 1993), that "periods of limitation in federal statutes . . . are universally regarded as nonjurisdictional." This refers, however, to time periods that are properly characterized as a statute of limitations, and not a limitation on judicial power. Examples of the latter include 28 U.S.C. sec. 2101 (specifying the time in which an appeal or a writ of certiorari must be filed with the Supreme Court) and Fed. R. App. P. 4 (specifying the time for filing a notice of appeal in the court of appeals). In those cases, the passage of too much time deprives the court of jurisdiction, regardless of what the parties may wish. On the other hand, a true statute of limitations may be waived by the parties' agreement or conduct.

The question is thus what kind of rule is established by sec. 1401: a limitations period, or a limit on judicial power? The fact that occasional opinions can be found calling sec. 1401 a "jurisdictional" statute is not dispositive, because some "jurisdictional" rules (such as those governing personal jurisdiction) really describe personal rights that can be waived, see Insurance Corp. of Ireland, Ltd. v. Compagnie des Bauxites de Guinee, 456 U.S. 694, 702 (1982), and others do not. Thus, we do not agree with Central States that the Third Circuit's passing reference to sec. 1401 as "jurisdictional" in Crown Cork and Seal, Inc. v. Central States, Southeast and Southwest Areas Pension Fund, 982 F.2d 857, 860 (3d Cir. 1992), resolves the matter. A closer look at Crown Cork and Seal shows that the court was describing the source of the federal question, not the question of the proper way to regard the 30-day time period. Our decision in Navco, holding that the general ERISA limitations period in sec. 1451(f) is not jurisdictional, is more directly on point. See Navco, 3 F.3d at 173. In addition, we note that the Supreme Court normally treats a statutory time period within which litigation must be commenced as non-jurisdictional. See, e.g., Irwin v. Department of Veterans Affairs, 498 U.S. 89, 95-96 (1990); Zipes v. Trans World Airlines, Inc., 455 U.S. 385, 393 (1982). We conclude that sec. 1401 should be treated the same way as sec. 1451(f), and thus that its 30- day period is better conceived of as a limitations period subject to the normal rules of waiver and estoppel.

Estoppel (or waiver) is Safeway's alternative argument to preserve its appeal, and we find it persuasive on these facts. In conjunction with its petition to the district court, Central States sent Safeway a letter to confirm that Safeway's local counsel would receive service of process. In that letter, Central States "agree[d] that Safeway has thirty days from today's date to answer or otherwise plead in response to this complaint." The letter was dated April 29, exactly 30 days before Safeway filed its counterclaim. We agree with Safeway that through this letter Central States waived any limitations objection it might otherwise have had. Both parts of this case (i.e. Safeway's effort to enforce the award, and Central States' challenge to it) are thus properly before us, and we can now turn to the merits.

The statutory and regulatory apparatus under which Central States was operating are not models of clarity--at least not to those who are uncomfortable operating in a world dominated by numbers and mathematical formulas. Nonetheless, neither Central States' actions nor Safeway's challenges will be comprehensible unless we take a moment to review the governing laws and regulations.

Safeway's asset sale resulted in a "partial withdrawal" for MPPAA purposes by virtue of 29 U.S.C. sec. 1385(a)(1), which imposes partial withdrawal liability for any plan year during which there is a "70 percent contribution decline." The first question is thus how a 70% contribution decline is calculated. Congress could have chosen to define this in a simple way- -if an employer's contribution is less than 30% of the prior year's level, then it incurs liability. This, however, would have caused problems for employers with relatively volatile year-to-year contributions but a consistent contribution pattern over time. In order to address that concern, Congress chose instead to create an eight-year rolling window divided into two parts: a three-year "testing" period that consists of the three most recent plan years and a five-year period (usually called the "lookback period"), which is comprised of the five plan years prior to the beginning of the testing period. See 29 U.S.C. sec. 1385(b)(1)(B). A partial withdrawal occurs when an employer's contribution level for every year during the testing period is lower than 30% of the average of the two highest contribution years during the lookback period. See 29 U.S.C. sec. 1385(b)(1)(A).

Although this method reduces problems related to business volatility, it introduces another problem. Because partial withdrawal liability is determined annually and independently of any prior partial withdrawals, an employer that permanently reduces its contribution levels as a result of an asset sale or other business change will probably incur withdrawal liability several times. The reason is that as years pass, the lookback period will continue to reach the pre- asset sale, high contribution years. This makes it likely that the testing period contribution levels (i.e. amounts paid in each of the most recent three years) will be less than 30% of the average of the two highest lookback years (i.e. the period from eight years ago through four years ago). That is what happened to Safeway. It sold its assets primarily in 1987 and 1988. Under these formulas, this meant that it first incurred withdrawal liability in 1990 (because the formula for partial withdrawal requires that the contribution level for every testing period year must be 70% less than the average of the two highest lookback years, so a few years have to pass before the employer becomes liable). At the end of 1993, the testing period was calendar years 1991, 1992, and 1993; the lookback period stretched all the way to 1986. Because Safeway had high contribution levels in 1986 and 1987 (i.e. before it sold its midwestern stores), it incurred partial withdrawal liability for 1993. (It also incurred such liability for 1991 and 1992, but it received a credit for its 1990 payment that covered the entire balance.)

In order to deal with the possibility that a withdrawing employer could be overburdened by application of the MPPAA partial withdrawal formula, Congress also provided a credit mechanism for partial withdrawal liability. Initially, this was a simple dollar-for-dollar credit for any amount previously paid to the plan. See 29 U.S.C. sec. 1386(b)(1). In Safeway's case, that would mean that it would receive a full credit against its 1993 liability for the $12.6 million that it paid Central States in conjunction with its 1990 withdrawal (here, of course, leaving no net payment due, because the 1993 charge was about $11.3 million). The dollar- for-dollar system, however, risked being too generous: liability for some additional UVBs would continue to accrue, even while some existing liabilities were satisfied. In other words, even if the total amount of UVBs remains the same, the composition of the liabilities will be different. Giving withdrawing employers a full credit for prior payments places all of the burden of new UVBs on remaining employers, which was precisely what the MPPAA was designed to prevent.

This wrinkle led Congress to authorize PBGC to issue regulations that "provide for proper adjustments in [the credit] . . . so that the liability for any complete or partial withdrawal in any subsequent year . . . properly reflects the employer's share of liability with respect to the plan." See 29 U.S.C. sec. 1386(b)(2). PBGC did so, with temporary regulations in 1987, which it finalized in 1992. Under these regulations, the credit phases out over time, thereby roughly capturing the change in the composition of the liability pool and allocating withdrawal liability accordingly. See generally 29 C.F.R. sec. 4206.1 et seq.

This, in general terms, is the system Central States was applying when it determined that Safeway was liable for a partial withdrawal in 1993. Safeway's opening argument is really a broadside attack on Congress's entire reasoning. Safeway points out that if it had withdrawn completely from Central States in 1988, it would have incurred only its liability for that year and an additional $135,000 in future liability. How, it asks, can it be rational for the statute and the PBGC regulations to impose nearly $2 million more in liability in 1993? This in its view cannot possibly "properly reflect" its share of liability to Central States for the UVBs, as required by sec. 1386(b)(2). It concludes that only the original dollar-for-dollar formula can be valid.

Given that Congress has entrusted PBGC with the responsibility of filling out the MPPAA's regulatory scheme, we review its work deferentially and will uphold its regulations if they are based on a permissible construction of the MPPAA. See, e.g., Production Workers' Union of Chicago and Vicinity v. NLRB, 161 F.3d 1047, 1050-51 (7th Cir. 1998). We consider those regulations here in the context of Safeway's challenge to their application.

Applying the rules for partial withdrawals, Central States concluded that Safeway was still liable for a partial withdrawal in 1993. It then applied a statutory formula to calculate the amount of the liability. Central States uses the "modified presumptive method" that is permitted under 29 U.S.C. sec. 1391(c)(2). Under this provision, a plan's UVBs are divided into two groups, which the parties call Pool 1 and Pool 2. Pool 1 liabilities are liabilities that were incurred before 1980 (when the MPPAA went into effect); Pool 2 consists of post-1980 liabilities. A particular employer's share of Pool 1 and Pool 2 liabilities is calculated separately; the sum of these two is the total withdrawal liability. The statutory verbiage is complicated, but in essence this is what happens: the employer's share is determined by multiplying each pool by the portion of all contributions to the plan made by the withdrawing employer for the last ten years of the pool in question (sec. 1391(c)(2) provides for five years, but Central States exercised its option under 29 U.S.C. sec. 1391(c)(5)(C) to lengthen this to ten years). In other words, Congress opted to allocate UVBs according to the relative size of an employer's contribution. PBGC followed this lead in the credit regulations, which also use a similar proportional method for determining the amount of an employer's credit. 29 C.F.R. sec. 4206.5.

The interaction of the various MPPAA formulas that are used to determine when a withdrawal occurs, the employer's share of liability in the event of a withdrawal, and the credit that an employer is to receive all contain some factors that in this instance worked to Safeway's disadvantage. For example, the amount of credit that Safeway receives for Pool 2 liabilities is reduced on a straight-line basis over, in this case, a ten-year period even though there is no similar reduction when liability is calculated in the first place. Compare 29 C.F.R. sec. 4206.5(b)(2) (reducing the credit) with 29 U.S.C. sec. 1391(c)(2)(C) (calculating the employer's share of Pool 2 liabilities). Along similar lines, 29 C.F.R. sec. 4206.5(b) (which provides the applicable methodology for calculating Safeway's credit, subject to the modification allowed by sec. 4206.9 for Central States' use of a ten-year period in calculating its allocation fractions) determines the amount of the credit on the basis of "the end of the plan year preceding the withdrawal for which the credit is being calculated." It appears that Central States interpreted the "withdrawal for which the credit was being calculated" as the 1993 withdrawal, meaning that it used that year's liability values. This is not the only possible reading of this regulation; perhaps the withdrawal to which the regulation refers is the 1990 withdrawal, in which case Safeway would receive a larger credit.

On appeal, Safeway does not mention either of these issues, so naturally any arguments relating to them are waived. International Union of Operating Engineers v. Rabine, 161 F.3d 427, 432 (7th Cir. 1998); Ricci v. Village of Arlington Heights, 116 F.3d 288, 292 (7th Cir. 1997). Instead, it focuses its energy on a single factor in its withdrawal liability calculation: the changing mixture of Pool 1 and Pool 2 liabilities in Central States' overall unfunded benefit levels from 1990 until 1993.

Safeway's major problem comes from the statutory method for determining the amount of Pool 1 and Pool 2 liabilities. At the end of any particular plan year, Central States' actuaries determine the total amount of UVBs by estimating the aggregate level of vested benefits and then comparing this to the plan's assets. Congress prescribed the formula for dividing these UVBs into Pool 1 and Pool 2. First, a plan amortizes its Pool 1 liabilities on a straight-line basis over 15 years, meaning that it takes the 1980 level, then reduces it by 1/15 for each year that has passed since 1980. (Note that this also means that the problem we face here is a disappearing one.) This reduction accounts for the commonsense intuition that the further one gets from 1980, the smaller the portion of total UVBs that are properly allocable to this period. Pool 2 is then defined as the residual amount of UVBs (i.e. total UVBs less Pool 1). As a consequence of this formula, a plan's total UVB level can remain constant while the mix between Pool 1 and Pool 2 changes (as Pool 1 gets amortized away).

In Safeway's case, this change in the mix of liabilities happened very quickly. Precisely how quickly is unclear from the record. Central States' assessment forms indicate that in 1990, Pool 1 comprised roughly 95.5% of total UVBs, whereas in 1993, Pool 1 had dropped to about 70% of the total. Safeway paints a much more dramatic picture, arguing that by 1993, Pool 1 represented only a trivial portion of total UVBs. The reasons for this apparent disagreement are not clear, but what matters in this case is the direction, not the magnitude, of the change. The reason that the change matters is because, as discussed above, liabilities and credits are calculated separately for each pool, then added together to determine an employer's net position. This means that in 1990 Safeway paid a lot of money based mostly on Pool 1 liabilities. Then, in 1993, Central States was entitled to take a fresh look at Safeway's withdrawal. The company's new liability and credit were then based on the new Pool 1 and Pool 2 levels. But since Pool 1 has shrunk, so has Safeway's credit. Meanwhile, its liability for Pool 2 increased. So Safeway owes again.

As we have already noted, Safeway's argument that it was entitled to a full credit for its 1990 payments rests on the assumption that it does not make any sense for it to incur withdrawal liability multiple times when it downsized only once. It believes that its predicament is just an unintended (and irrational) consequence of the rote application of the MPPAA's formula for determining when a partial withdrawal occurs. To the extent Safeway argues that multiple instances of partial withdrawal liability are patently irrational and that the PBGC regulations are invalid if they fail to correct the problem, we disagree. Far from being a freak occurrence, multiple instances of withdrawal liability are virtually guaranteed by application of the sec. 1385 formula, and the formula itself was rationally designed to address a number of problems with multiple employer plans. Congress was aware that sequential payments would be required, as the numerical example that appears in the MPPAA's legislative history shows. See H.R. Rep. No. 96-869, pt. 2, at 51 (1980). Consequently, we reject any notion that the PBGC credit regulations must fully correct for multiple instances of partial withdrawal liability that arise out of the same business event. Rather, our focus is on the particulars of Safeway's problem and the credit method's treatment of its case.

Safeway decries the change in the mix of Central States' UVBs, calling it a "spillover" of liabilities from Pool 1 into Pool 2. Safeway maintains that these are really the same UVBs, that nothing meaningful happened between 1990 and 1993, and that the conversion from Pool 1 to Pool 2 is just an accounting fiction for which it should not have to pay. But something important did happen: time passed. And as time passed, the mix of Central States' UVB pool changed substantially. In 1990, most of the UVBs were "old" (pre-1980), whereas in 1993 many more of them were "new" (post-1980). It is true that this is primarily a product of the accounting method that Congress chose to age the benefits, but the same could be said of any attribution of benefits to a particular plan year or set of years. (We also see nothing that would systematically harm all employers; the movement from one pool to another will cause some to gain and others to lose, depending on the composition and stability of the workforce.)

Some method is necessary to handle the aging of benefits; otherwise, there will be no match between the time during which an employer participated in a plan and the liabilities for which it is responsible. Congress chose a very simple method, placing a plan's liabilities into one of two categories: old (i.e. Pool 1) and new (i.e. Pool 2). Furthermore, it picked a simple method for determining the portion of total UVBs properly included in each of the pools: 15-year straight-line amortization. Over time, the proportion attributable to each pool will inevitably change, as it did here. It would be easy to scoff at this as accounting fiction since the coarseness of the actuarial method is so apparent. And certainly Congress could have come up with (or could have had PBGC come up with) more sophisticated methods that would more perfectly match a plan's UVBs with a particular plan year. But it is only accounting fiction because Safeway is unhappy with the result. Everywhere else, it is just accounting.

Safeway's position, then, boils down to a claim that the regulations are unreasonable for failing to correct the actuarial imperfections in the system for aging benefits that Congress authorized plans such as Central States to use. We see nothing in sec. 1386(b)(2) that places such a heavy burden on PBGC. As our discussion of the methods underlying the calculation of MPPAA withdrawal liability shows, there are a variety of assumptions and tradeoffs implicit in this system. One of these is a simplified method for aging a plan's UVBs. Section 1386(b)(2) requires the regulations to adjust an employer's credit so that it "properly reflects" the employer's liability, but this mandate must be read in light of the other provisions of the MPPAA, including sec. 1391(c)(2)'s approach to aging benefits. The PBGC regulations appear to do a fairly good (or at least not unreasonable) job of following Congress's simple actuarial method, insofar as the same division (between old and new UVBs) is used to determine both liability and credit. There is no irrationality in PBGC's decision to apply the same rules on both the liability and credit sides of the fence. While a more complicated method might help Safeway, Congress was not compelled to choose one. Because PBGC was not under an obligation to make an imperfect system perfect, it was by the same token not under an obligation in Safeway's case to reverse what Safeway calls the spillover from Pool 1 into Pool 2.

Next, Safeway argues that the district court reached an entirely wrong conclusion because it applied the wrong regulation in the first place. Central States now agrees, though the two sides see radically different results stemming from this argument. The fund argues that the applicable regulation is 29 C.F.R. sec. 4206.5. This section provides the credit method for plans that use the modified presumptive method for determining liability. The modified presumptive method normally looks back five years in determining an employer's partial withdrawal liability. See 29 U.S.C. sec. 1391(c)(2)(B) and (C). As we have noted, Central States took advantage of a provision that allowed it to extend this five-year window to ten years. 29 U.S.C. sec. 1391(c)(5). This difference led the district court to choose 29 C.F.R. sec. 4206.9, which covers plans that have "adopted an alternative method of allocating unfunded vested benefits pursuant to [29 U.S.C. sec. 1391(c)(5)]." Under the regulation, plans must adopt credit methods "consistent with the rules in [29 C.F.R.] sec.sec. 4206.4 through 4206.8 for plans using the statutory allocation method most similar to the plan's alternative allocation method." If this section applies, the upshot is that Central States should use the method that appears in sec. 4206.5, but with a modification for its use of the ten-year period. The difference between using the five- and ten-year windows isn't trivial. If Central States is allowed to use the five-year period, it is entitled to another $225,000. Safeway teams up with Central States in attacking the district court's acceptance of 29 C.F.R. sec. 4206.9, but, unsurprisingly, draws a very different conclusion from its inapplicability. Safeway maintains that none of the regulatory methods prescribed by PBGC is applicable, thereby creating a sort of "regulatory limbo." Absent a governing regulation, Safeway maintains that we must go back to the statutory standby, which was the dollar-for-dollar credit of 29 U.S.C. sec. 1386(b)(1). Since Safeway paid $12.6 million in connection with its 1990 partial withdrawal and Central States' assessment for 1993 was only $11.3 million, it would owe nothing under this rule.

The district court concluded that the "alternative method" regulation applied (and thus that Central States was obliged to stick with the ten-year period it had formally chosen) because it refers to the "alternative method of allocating unfunded vested benefits pursuant to [29 U.S.C. sec. 1391(c)(5)]." 29 C.F.R. sec. 4206.9. The statutory provision that allows Central States to use a ten- rather than five- year window is 29 U.S.C. sec. 1391(c)(5)(C) (allowing plans to use any period between five and ten years for computing the various statutory fractions), meaning that the regulation applies on its face. Notwithstanding the fact that the regulation refers to all of sec. 1391(c)(5), Safeway and Central States both argue that PBGC really meant to refer only to subsections (A) and (B), not (C). Their main support for this contention is that the words "alternative methods" appear in (A) and (B) but not (C).

The arbitrator accepted this argument, but, like the district court, we are not convinced. First, neither sec. 1391(c) (5)(A) or (B) actually prescribes an alternative method. Rather, (A) simply gives PBGC the authority to approve alternative methods for determining liability that the plans themselves create. Likewise, (B) authorizes PBGC to issue standardized approaches to permit plans to create their own methods of assessing liability without the need for specific PBGC approval. Neither actually creates an alternative method. Both relate instead to precisely the same issue that subsection (C) covers, which is the authority of plans to modify their method of determining liability. No one has suggested a good reason not to take sec. 4206.9 at face value.

Second, and more importantly, the reading the district court chose avoids the strange results that would flow from either Safeway's or Central States' position. Safeway's argument (that no section applies and that, consequently, the dollar-for-dollar approach governs) creates an enormous loophole in an otherwise comprehensive regulation that PBGC spent more than five years developing. Central States' (post-litigation) position (that sec. 4206.5's five-year credit amortization applies) makes equally little sense. If a plan is using a ten-year window to determine liability (which Central States is not willing to give up), it should also use a ten-year period to determine an employer's credit. That is the overall point of sec. 4206.9, which directs plans that do not follow one of the statutory methods for computing withdrawal liability to adapt their credit mechanisms accordingly. That was also Central States' pre-litigation understanding of the regulation, as evidenced by its adoption of a credit rule that uses a ten-year amortization period. Given all of that, we conclude that sec. 4206.9 applies, and Central States' original assessment used the correct regulation.

Failing all other possible avenues of attack, Safeway turns to the Constitution. It argues that the effect of the partial withdrawal liability credit regulations is so unfairly skewed against it as to amount to an unconstitutional taking. Pointing to Connolly v. Pension Benefit Guarantee Corp., 475 U.S. 211 (1986), which upheld the MPPAA against a takings challenge rooted in the employer's contract with the plan, Safeway relies on a concurrence in which two members of the Court suggested that "the imposition of withdrawal liability under the MPPAA . . . may in some circumstances be so arbitrary and irrational as to violate the Due Process Clause of the Fifth Amendment." 475 U.S. at 228 (O'Connor, J., concurring). This is just the case Justice O'Connor had in mind, Safeway tells us. But it is important to note what Safeway has not argued. It has not challenged the constitutionality of the actuarial method used to age unfunded benefits in the first place. Rather, its argument is that the PBGC regulations are unconstitutional for failing to correct adequately for what it perceives as distortions in the calculation of partial withdrawal liability. By itself, this is an uphill battle. The real death knell for Safeway's position, however, is sounded by the statutory requirement that any PBGC method used to determine an employer's credit "properly reflect the employer's share of liability with respect to the plan." 29 U.S.C. sec. 1386(b)(2). The Connolly concurrence suggests the possibility of lurking Due Process and Takings concerns where MPPAA withdrawal provisions "may lead to extremely harsh results" that are "not easily traceable to the employer's conduct." 475 U.S. at 235 (O'Connor, J., concurring). Since sec. 1386(b)(2) cabins PBGC's discretion and instructs it to create regulations that "properly reflect" an employer's share, a set of regulations that passes the statutory test will, therefore, also pass constitutional muster. For the reasons we have already described, we conclude that the set of possibilities allowed by sec. 1386(b)(2) and reflected in the regulations is a subset of all constitutionally permissible regulations. Our conclusion that the regulation is within PBGC's statutory authority therefore also resolves the constitutional question against Safeway.

Safeway makes two final arguments. First, Safeway argues that a provision of the agreement settling the 1990 demand precludes Central States' current claim. Second, it claims that Central States is estopped from making a change away from the dollar-for-dollar system, because of some oral representations an employee made in June 1992. For the reasons stated by the district court, we find these points and any others Safeway has presented here that we have not specifically discussed to be without merit.

It is easy to understand why Safeway regards itself as a victim of circumstances. The timing of its midwestern asset sales, along with the many approximations and balances that are part of the MPPAA's attempt to regulate the enormously complex area of multiemployer pensions (the manner in which the MPPAA "ages" an employer's liabilities, the possibility of successive partial withdrawals as a result of the three-year testing and five-year lookback periods, and Congress's decision to allow plans to use ten years of contribution history to determine an employer's allocable share), all combined to produce an expensive result. But we cannot say that it was a fundamentally unfair result, nor a result outside the boundaries of the statutes and regulations. We therefore Affirm the judgment of the district court.