BOUDIN, Circuit Judge.

Bath Iron Works, Inc. (“Bath”) is a Maine corporation that has long engaged in shipbuilding and the repair of ships. It has employees who are covered by the Long-shore and Harbor Workers’ Compensation Act, 33 U.S.C. §§ 901-50 (the “Longshore Act”). That statute enacts an extensive workers’ compensation program that protects longshore and other specific classes of workers whose injuries occur upon navigable waters of the United States or adjoining facilities like piers and dry docks. Id. § 903(a).

For the most part, scheduled payments for death or disability are made either by the employer or under insurance coverage; Bath, as it happens, is a self-insurer. But Congress has also included in the Longshore Act a so-called “special fund,” 33 U.S.C. § 944, administered by the Secretary of Labor (“the Secretary”). The fund is used for various purposes — most importantly, for “second injury” or “section 8(f)” payments-made under 33 U.S.C. § 908(f), a provision described below. See 33 U.S.C. § 944(i). The special fund is primarily funded by annual assessments levied by the Secretary on employers subject to the Longshore Act. Id. § 944(c). 1

In this case the Secretary brought suit against Bath in the district court to recover supplemental assessments for the special fund claimed to be due by the Secretary. 838 F.Supp. 650. Because the dispute involves Bath’s obligation to the special fund, the statutory formula used to determine such obligations — 33 U.S.C. § 944(c)(2) — needs to be explained. First, the statute requires the Secretary to estimate the fund’s expected obligations for the forthcoming year, including expected section 8(f) payments. Id. Then, the Secretary estimates other fund income (e.g., fines) and levies the balance by assessing employers. Id. Specifically, the Secretary fixes and assesses each employer’s share under a formula that takes the average of two fractions, both of which use the prior year’s experience as a base. Id.

One fraction is the ratio of the individual employer’s workers’ compensation payments “under this chapter” [the Longshore Act] during the prior year to all such payments by all employers under the chapter during that year. 33 U.S.C. § 944(c)(2)(A). The other fraction is the ratio of the section 8(f) payments attributable to the employer during the prior year to all such section 8(f) pay *76 ments attributable to all employers for that year. Id. § 944(e)(2)(B). In brief, the employer’s obligation is based in part on its own prior payment experience and in part on the special fund’s experience in making section 8(f) payments to that employer’s employees.

For example, if Bath’s compensation payments under the Longshore Act for 1988 represented three percent of all such employer payments for that year, and the special section 8(f) payments for Bath employees represented one percent of all such section 8(f) payments for that year, Bath’s assessment would be two percent of the (otherwise unfunded) special fund obligations for 1989, as estimated by the Secretary. Under such a formula, every employer has an interest in seeing its own workers’ compensation payments “under this chapter” represented by as small a figure as possible. The lower the figure, the more the burden of financing the special fund is shifted to other employers.

The present case arose because Bath calculated its own assessment by excluding from the formula calculation under section 944(c)(2)(A) most payments it made to injured employees who were covered both by the Longshore Act and the Maine Workers Compensation Act. Me.Rev.Stat.Ann. tit. 39, § 1 et seq. The Maine statute generally provides comparable payments, and both regimes encourage the employer to make payment without having the employee file a formal claim. Where both statutes covered the same injury in the same amount, Bath said that it was making payment under the Maine statute and filed a boilerplate denial of liability under the Longshore Act. See 33 U.S.C. § 914(d).

An employer’s payment of workers’ compensation under a state statute discharges the employer’s liability pro tanto under the Longshore Act. This was well settled by court decision long ago and eventually Congress enacted a provision to this effect. 33 U.S.C. § 903(e). Thus, in such dual liability cases, Bath’s payments — purportedly under the Maine statute — erased its liability under the federal statute as well. This erasure of federal obligations led the Secretary to recalculate Bath’s formula assessment on the premise that such dual liability payments should be treated as ones made “under” the Longshore Act. Bath disagreed. The Secretary brought suit.

In the district court, the magistrate judge entered a recommended decision in favor of Bath, and the district court approved the recommendation and dismissed the Secretary’s complaint. The gist of the district court’s decision was that the language of the formula — specifically, its reference to an employer’s payments made “under this chapter” — was clear and unambiguous. “The subsection [944(c)(2)(A) ],” said the district court, “speaks in terms of payments, not liability”; and it deemed the dual liability payments in dispute to be ones made under Maine law, not the Longshore Act. The court also relied secondarily on legislative history and policy.

On this appeal, the Secretary takes the position that his own reading of the formula language is at least permissible, is a reasonable one, and is entitled to the deference ordinarily due to the agency or department under the Chevron doctrine. Chevron v. NRDC, 467 U.S. 837, 104 S.Ct. 2778, 81 L.Ed.2d 694 (1984). We generally agree with the Secretary that the statutory language permits his reading, which is entitled to a measure of deference. We also think that the history of the provision supports the Secretary’s reading. Finally, there is no clue anywhere that the distinction proposed by Bath was ever considered, let alone adopted, by Congress.

Starting with statutory language, the parties devote many pages to the question whether the disputed payments are, in a literal sense or by various characteristics, payments “under” the Longshore Act. We do not think that the bare words “under this chapter” are precise enough to resolve orn-ease. As a matter of dictionary meaning, the phrase could (as Bath claims) refer to the statute invoked by the payor when making the payment — here, the Maine statute — or it could (as the Secretary claims) cover any payment that erases or discharges a liability that otherwise exists under the federal statute, regardless of what the payor says when handing over the money.

*77 The surrounding circumstances seem to us equally uninformative. It makes no difference to any known purpose of Congress, or any suggested policy underlying the statute, that Bath did, as it claims, file repeated boilerplate notices of contravention denying liability under the federal statute. Conversely, it does not matter whether, as the Secretary claims, Bath reported the accidents in question to federal authorities, as other provisions required it to do. These arguments are examples of fussing about inessentials.

What matters, given that the statute’s language is open to more than one reading, is the history and purpose of the provision. Congress adopted an earlier version of this formula in 1972 when the assessment device was first adopted to support the special fund. Under the 1972 amendments, the assessment was based on the proportion of the employer’s prior year “payments made on risks covered by this Act” to “the total of such payments made by all” employers. 86 Stat. 1251, 1256. This is a variation, of course, on the language now comprising the first half of the statutory formula. Compare 33 U.S.C. § 944(c)(2)(A).

In recent years, the main use of the special fund has been to encourage employers to hire workers who have suffered a previous partial permanent disability. For various reasons, employers feared that such a worker who suffered a new disability might impose extra liability on the employer where the first injury contributed to the severity of the second; a good example is the loss of an eye by a worker already blind in one eye. See Lawson v. Suwannee Fruit & Steamship Co., 336 U.S. 198, 69 S.Ct. 503, 93 L.Ed. 611 (1949); 2. A. Larson, Workmen’s Compensation Law § 59.31(a) (1994). The section 8(f) regime was designed to lessen this discouragement.

For some years, section 8(f) has accomplished this end by making the special fund, and not the employer, hable in certain circumstances. for so-called “second-injury” compensation payments, beginning after 104 weeks of employer' payments. 33 U.S.C. § 908(f). In 1972, when Congress first adopted the employer assessment device to support the special fund, it also greatly enlarged the scope of the fund’s liability by inter alia extending the fund’s liability retroactively to provide some coverage for some second injuries that had occurred prior to the new statutory amendments.

What Congress discovered between 1972 and 1984 is that employers were “dumping” as many cases as possible in the section 8(f) basket. This meant that the employer not only avoided compensation liability to the worker after 104 weeks (as intended) but also (unexpectedly) lowered the employer’s future formula payments to the special fund below the level that would otherwise have applied. The lowering occurred because the original 1972 formula only counted payments by the employer as increasing the employer’s fraction; section 8(f) payments made by the fund, on account of the employer’s double-injury employees, did not increase the employer’s assessment.

Under the new section 944(c)(2) formula adopted in 1984 and in force today, the payments by the fund on account of these double-injury employees is now attributed to the employer to the extent that such payments increase the employer’s assessment under the second half of the formula. This second half represents only 50 percent of the final assessment; thus the employer gets some help when the fund takes over compensation and, presumably, the employer retains some incentive to hire the partly disabled. But the employer does see its future assessments rise somewhat as the employer transfers responsibility to the special fund.

As Congress saw it, “[t]his [new] formula will, at once, dissuade the dumping of cases into the fund, and will more equitably apportion the responsibility of paying for the fund.” 130 Cong.Ree. 25,904 (1984) (statement of Mr. Miller). 2 Further, because the employer now has a continuing (albeit indirect) interest in holding down unjustified *78 payments to employees even after 104 weeks, the legislators expected that unjustified disability claims would be better policed than they had been by the fund administrators. Id. Other explanations for the change are consistent. 130 Cong.Ree. 26,297 (1984) (statement of Senator NieWes).

In sum, prior to 1984 Congress intended the special fund to be paid for by employers primarily in proportion to their experience in paying compensation claims required to be paid by the federal statute (“payments made on risks covered by [the] Act”). No reason is suggested to us why Congress might have wished in 1984 to lower an employer’s share because, by happenstance, the employer was located in a state with generous compensation laws of its own and the employer chose to pin a state label on its payment while discharging an obligation that existed under both federal and -state law. By the same token, no legislative evidence indicates that Congress intended to make such a change in 1984.

Bath infers such an intent because Congress in 1984 altered the 1972 phrase “payments made on risks covered by [the] Act” to refer instead to payments “under this chapter.” As best we can tell, Congress happened by chance to alter the wording of the original 1972 sentence when — in a last-minute compromise (see note 2, supra) — it adopted the 1972 provision as the first part of the new two-part formula. To the extent that the 1972 language is slightly more helpful to the Secretary, it strengthens the Secretary’s present position slightly, rather than detracts from it, precisely because there is no indication that Congress meant to change the substance of that part of the formula.

There is only one discrepancy that gives us any pause. In 1991, the Secretary’s Benefits Review Board rendered a decision in a case entitled Stewart v. Bath Iron Works Corp., 25 B.R.B.S. 151 (1991). There, it appears that a second-injury employee of Bath withdrew a claim for compensation under the Longshore Act when Maine’s benefits proved more generous. Although the Stewart opinion is difficult to decipher without more information, the Board apparently took the view that section 8(f) relief from the special fund was not available to Bath because the payments that Bath was making to the employee were required of Bath by the Maine statute but not by federal law.

Bath argued to the district court, and repeats here, its claim that “it would be anomalous to base [Bath’s] special fund assessments on state law payments, when special fund relief is not available to [Bath] from its obligations under the Maine [compensation law].” The technical responses offered in the government’s reply brief may explain why the district court saw some merit in Bath’s reliance on Stewart. The government’s failure either to answer Bath’s central argument, or to concede the discrepancy, is not what we would expect from government counsel.

Bath’s argument is relevant in the sense that a construction that produces anomalous results is, by that fact alone, a more doubtful reading of a statute. Public Employees Retirement Sys. of Ohio v. Betts, 492 U.S. 158, 177-78, 109 S.Ct. 2854, 2866-67, 106 L.Ed.2d 134 (1989). Still, nothing in Stewart is literally inconsistent with-the government’s reading of the assessment formula; Stewart turns on a reading of other provisions of the Longshore Act that are not centrally involved in this case. At worst, Stewart— assuming it was correctly decided — produces an apparent possible inequity of a kind that is not unknown in complex statutory arrangements. Puerto Rico Telephone Co. v. FCC, 553 F.2d 694, 700 (1st Cir.1977).

We have far too little information to assess fully the dense and elliptical opinion in Stewart. The case may have been wrongly decided; or the anomaly may be a rarity that carries no great weight in interpreting the formula provisions before us; or it may not be an inequity at all (the Board in Stewart refers to the possibility that Bath could seek relief from Maine’s counterpart to the special fund provision). Bath gives us no information on any of these matters, so there is no reason to feel distress on its behalf in having to leave this dangling loose end.

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

Notes

. The statute refers to contributions by self-insured employers or carriers; but for simplicity we refer to "employers” throughout the opinion.

. The statutory solution ultimately devised by Congress was adopted late in the day by the Conference Committee and explained only in floor statements. Compare H.Rep. No. 98-570, 98th Cong., 1st Sess. 20-21 (1983), with Conf. Rep. No. 98-1027, 98th Cong., 2d Sess. 31 (1984).