POSNER, Circuit Judge.
Melvin Bullard appeals from a judgment for the defendants, Sercon Corporation and Local 81 of the International Laborers’ Union, entered after a bench trial in which Bullard tried to prove that the defendants had discriminated against him because of his race, in violation of Title VII of the Civil Rights Act of 1964, 42 U.S.C. §§ 2000e et seq., and 42 U.S.C. § 1981. Bullard was employed by Sercon, which had a contract with Bethlehem Steel Corporation to maintain various facilities at Bethlehem’s steel works in Burns Harbor, Indiana. Between 1977 and his layoff on April 30, 1982, Bul-lard worked at the coke ovens. At the time of his layoff he was one of a crew of 10 or 11 workers, four of whom, including Bul-lard, were black. In 1982 Bethlehem closed one of the coke ovens for repairs, and as a result fewer workers were needed at the ovens. Jim Lehner, Bethlehem’s maintenance foreman at the Burns Harbor works, decided that Bullard should go, because he was a slow worker and was spending too much time in the bathroom. Bullard was not the least senior member of the crew, but, oddly, Sercon's contract with Local 81 gave workers no rights based on seniority. Sercon did not assign Bullard to any other work, instead placing him on indefinite layoff status from which he has never been recalled.
In arguing that Sercon’s failure to assign him to other work at the Bums Harbor Works was due to his being black, Bullard notes that only 13 of the 117 workers whom Sercon employed at the Bums Harbor works in 1982 — 11 percent — were black although 41 percent of Local 81’s members were black. Bullard had never been disciplined or formally warned about being too slow (though there was testimony that he had once been told to “speed it up a little”), and his supervisor at Sercon testified that Bullard was a good worker and would have been reassigned had the union referred him. Although 1982 saw a drastic reduction in the number of hours that Sercon’s employees put in at the Bums Harbor works (April in particular was a big month for layoffs), foremen’s reports show, according to Bullard, that there was work that he could have done in other departments served by Sercon at the Bums Harbor works.
[466]*466The district judge disagreed with Bullard’s version, and we cannot say that his findings of fact, and his conclusion (which for purposes of appellate review is also a finding of fact, Pullman-Standard v. Swint, 456 U.S. 273, 102 S.Ct. 1781, 72 L.Ed.2d 66 (1982)) that Bullard’s layoff was not due to his race, were clearly erroneous. As Bullard virtually concedes, we must accept the judge’s decision to believe Leh-ner’s testimony that, forced to lay off a worker at the coke ovens, he picked Bul-lard because he was the slowest worker and not because Lehner wanted to protect the white workers’ jobs. Appellate review of credibility determinations is severely limited. We shall reject a district judge’s decision to believe oral testimony only where the testimony is seriously inconsistent internally, or contrary to established laws of nature or otherwise fantastic, or irreconcilably in conflict with indubitable documentary or physical evidence, stipulations of fact, admissions, or evidence of equivalent certainty. See Anderson v. City of Bessemer City, 470 U.S. 564, 575, 105 S.Ct. 1504, 1512, 84 L.Ed.2d 518 (1985). None of these circumstances is present in this case.
Even if we could say that Lehner was lying, this would not carry the day for Bullard-indeed, might advance his case very little. Lehner was not an employee o Sercon. Since his employer, Bethlehem Steel Corporation, is not a defendant, we need not decide whether Bethlehem might have been the indirect employer of both Lehner and Bullard and hence both a proper defendant in a Title VII suit (see the discussion of that issue in Shrock v. Altru Nurses Registry, 810 F.2d 658, 660 (7th Cir.1987)) and one chargeable with responsibility for Lehner's conduct. Whether Lehner had good or bad, racist or innocent, reasons for choosing Bullard to lay off when it became necessary to lay off a member of the crew at the coke ovens, the layoff of Bullard was beyond Sercon's control. Sercon's culpability, if any, depends on what it did when confronted by Lehner's action. Sercon apparently was doing other work at Bethlehem's Burns Harbor plant that Bullard could have been assigned to; if the reason, or a reason, for not assigning him-for instead placing him on permanent layoff status-was that he was black, Ser-con was guilty of racial discrimination.
Bullard argues that since there is no evidence that Sercon itself regarded him as a slow or otherwise substandard worker, its failure to reassign him to work elsewhere in the plant when Lehner ejected him from the coke ovens must have been based on his race. But this is a non sequi-tur. The fact that a black worker is fired or laid off without good cause does not establish racial discrimination. It may in some cases be evidence of discrimination, see, e.g., Pollard v. Rea Magnet Wire Co., 824 F.2d 557, 559 (7th Cir.1987); cf. Graefenhain v. Pabst Brewing Co., 827 F.2d 13, 18 (7th Cir.1987), and circumstantial evidence plays an essential role in proving discrimination, see, e.g., Riordan v. Kempiners, 831 F.2d 690, 697-98 (7th Cir.1987). But it would count for little in a case like this. Bullard had been removed from his usual work station by a decision (Lehner’s) over which Sercon had no control, and Ser-con’s work force at the plant was shrinking. In these circumstances, there was nothing suspicious in the fact that Bullard was not given another assignment but instead was placed on a layoff status that proved to be permanent.
Granted, if Bullard had proved that Sercon replaced him with a white, Sercon would have had to produce a nondiscriminatory reason for its action, or lose. See McDonnell-Douglas Corp. v. Green, 411 U.S. 792, 93 S.Ct. 1817, 36 L.Ed.2d 668 (1973). At trial Bullard attempted to prove that he had been replaced in his crew at the work ovens by a white. This proof, however, was beside the point; Lehner controlled assignments to the crew, and his decisions cannot be attributed to Sercon. Anyway the district court found on adequate evidence that Bullard had not been replaced by anyone; the crew simply shrank in number.
Bullard could have tried to show that whites who were made redundant by the reduction in demand for Sercon’s services, [467]*467but not blacks like him, were reassigned rather than laid off. This line of attack was not taken in the district court, however, and it is therefore too late to press it in this court.
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POSNER, Circuit Judge.
Melvin Bullard appeals from a judgment for the defendants, Sercon Corporation and Local 81 of the International Laborers’ Union, entered after a bench trial in which Bullard tried to prove that the defendants had discriminated against him because of his race, in violation of Title VII of the Civil Rights Act of 1964, 42 U.S.C. §§ 2000e et seq., and 42 U.S.C. § 1981. Bullard was employed by Sercon, which had a contract with Bethlehem Steel Corporation to maintain various facilities at Bethlehem’s steel works in Burns Harbor, Indiana. Between 1977 and his layoff on April 30, 1982, Bul-lard worked at the coke ovens. At the time of his layoff he was one of a crew of 10 or 11 workers, four of whom, including Bul-lard, were black. In 1982 Bethlehem closed one of the coke ovens for repairs, and as a result fewer workers were needed at the ovens. Jim Lehner, Bethlehem’s maintenance foreman at the Burns Harbor works, decided that Bullard should go, because he was a slow worker and was spending too much time in the bathroom. Bullard was not the least senior member of the crew, but, oddly, Sercon's contract with Local 81 gave workers no rights based on seniority. Sercon did not assign Bullard to any other work, instead placing him on indefinite layoff status from which he has never been recalled.
In arguing that Sercon’s failure to assign him to other work at the Bums Harbor Works was due to his being black, Bullard notes that only 13 of the 117 workers whom Sercon employed at the Bums Harbor works in 1982 — 11 percent — were black although 41 percent of Local 81’s members were black. Bullard had never been disciplined or formally warned about being too slow (though there was testimony that he had once been told to “speed it up a little”), and his supervisor at Sercon testified that Bullard was a good worker and would have been reassigned had the union referred him. Although 1982 saw a drastic reduction in the number of hours that Sercon’s employees put in at the Bums Harbor works (April in particular was a big month for layoffs), foremen’s reports show, according to Bullard, that there was work that he could have done in other departments served by Sercon at the Bums Harbor works.
[466]*466The district judge disagreed with Bullard’s version, and we cannot say that his findings of fact, and his conclusion (which for purposes of appellate review is also a finding of fact, Pullman-Standard v. Swint, 456 U.S. 273, 102 S.Ct. 1781, 72 L.Ed.2d 66 (1982)) that Bullard’s layoff was not due to his race, were clearly erroneous. As Bullard virtually concedes, we must accept the judge’s decision to believe Leh-ner’s testimony that, forced to lay off a worker at the coke ovens, he picked Bul-lard because he was the slowest worker and not because Lehner wanted to protect the white workers’ jobs. Appellate review of credibility determinations is severely limited. We shall reject a district judge’s decision to believe oral testimony only where the testimony is seriously inconsistent internally, or contrary to established laws of nature or otherwise fantastic, or irreconcilably in conflict with indubitable documentary or physical evidence, stipulations of fact, admissions, or evidence of equivalent certainty. See Anderson v. City of Bessemer City, 470 U.S. 564, 575, 105 S.Ct. 1504, 1512, 84 L.Ed.2d 518 (1985). None of these circumstances is present in this case.
Even if we could say that Lehner was lying, this would not carry the day for Bullard-indeed, might advance his case very little. Lehner was not an employee o Sercon. Since his employer, Bethlehem Steel Corporation, is not a defendant, we need not decide whether Bethlehem might have been the indirect employer of both Lehner and Bullard and hence both a proper defendant in a Title VII suit (see the discussion of that issue in Shrock v. Altru Nurses Registry, 810 F.2d 658, 660 (7th Cir.1987)) and one chargeable with responsibility for Lehner's conduct. Whether Lehner had good or bad, racist or innocent, reasons for choosing Bullard to lay off when it became necessary to lay off a member of the crew at the coke ovens, the layoff of Bullard was beyond Sercon's control. Sercon's culpability, if any, depends on what it did when confronted by Lehner's action. Sercon apparently was doing other work at Bethlehem's Burns Harbor plant that Bullard could have been assigned to; if the reason, or a reason, for not assigning him-for instead placing him on permanent layoff status-was that he was black, Ser-con was guilty of racial discrimination.
Bullard argues that since there is no evidence that Sercon itself regarded him as a slow or otherwise substandard worker, its failure to reassign him to work elsewhere in the plant when Lehner ejected him from the coke ovens must have been based on his race. But this is a non sequi-tur. The fact that a black worker is fired or laid off without good cause does not establish racial discrimination. It may in some cases be evidence of discrimination, see, e.g., Pollard v. Rea Magnet Wire Co., 824 F.2d 557, 559 (7th Cir.1987); cf. Graefenhain v. Pabst Brewing Co., 827 F.2d 13, 18 (7th Cir.1987), and circumstantial evidence plays an essential role in proving discrimination, see, e.g., Riordan v. Kempiners, 831 F.2d 690, 697-98 (7th Cir.1987). But it would count for little in a case like this. Bullard had been removed from his usual work station by a decision (Lehner’s) over which Sercon had no control, and Ser-con’s work force at the plant was shrinking. In these circumstances, there was nothing suspicious in the fact that Bullard was not given another assignment but instead was placed on a layoff status that proved to be permanent.
Granted, if Bullard had proved that Sercon replaced him with a white, Sercon would have had to produce a nondiscriminatory reason for its action, or lose. See McDonnell-Douglas Corp. v. Green, 411 U.S. 792, 93 S.Ct. 1817, 36 L.Ed.2d 668 (1973). At trial Bullard attempted to prove that he had been replaced in his crew at the work ovens by a white. This proof, however, was beside the point; Lehner controlled assignments to the crew, and his decisions cannot be attributed to Sercon. Anyway the district court found on adequate evidence that Bullard had not been replaced by anyone; the crew simply shrank in number.
Bullard could have tried to show that whites who were made redundant by the reduction in demand for Sercon’s services, [467]*467but not blacks like him, were reassigned rather than laid off. This line of attack was not taken in the district court, however, and it is therefore too late to press it in this court. Bullard’s counsel has cited us to foremen’s reports in the district court record that she says show that there was other work in the plant and that it was given to whites instead of to Bullard. But, so far as we are able to tell, she has not made the reports a part of the record on appeal, and we doubt whether they indicate the race of the workers listed in them. Without the benefit of an adversarial process we are unable to draw our own factual inferences from the reports, let alone use them to conclude that the district judge committed a clear error in ruling in favor of Sercon.
We turn to Bullard’s Title VII case against the union. See 42 U.S.C. § 2000e-2(c). Local 81 runs a nonexclusive hiring hall — meaning that employers, even if they have a collective bargaining contract with the union, do not have to hire from the hall and workers are free to seek work on their own outside of the referral system. Nevertheless, when workers who belong to the union (as Bullard did when he was laid off by Sercon) are laid off, they usually register with the hiring hall. Bul-lard did, and in June 1982 was referred to a construction company where he worked until being laid off in September of that year. He kept calling the hiring hall for additional referrals, but received none. In January 1983, Virgil Goin, the union’s business manager, told Bullard that he would get no more referrals, because he was no longer a member of the union in good standing, not having paid dues since November 1982.
Bullard’s story is different. He testified that in May 1982, the month after he had been laid off by Sercon, he filed a grievance against Sercon with the union, and Goin refused to prosecute it. When Bul-lard threatened to sue the union, Goin told him (again according to Bullard’s testimony) that if Bullard sued he would never work in construction again. As a result, says Bullard, he did not file administrative charges against the union, instead bringing this suit against both Sercon and the union in 1983 after he had given up any hope of job referrals from the union’s hiring hall. Bullard produced testimony from other union members that Goin was hostile to blacks, testimony that Goin referred jobs to whites and not blacks — including whites who, just like Bullard, were delinquent in their dues — and testimony that Goin was trying to make the union “whiter.” Although the union was, as we said, 41 percent black, 95 percent of the members under 30 were white. (The figure for blacks is for 1982, that for young whites for 1986, by which time the percentage of blacks in the union had fallen to 17.) The district judge found no racial discrimination, another finding that Bullard asks us to set aside as being clearly erroneous.
The union asks us not to reach that issue, arguing that the suit against it is barred by Bullard’s failure to file an administrative complaint with the Equal Employment Opportunity Commission, which Title VII requires as a condition precedent to bringing suit, 42 U.S.C. § 2000e-5(e). Bullard counters that if the union wanted to alter the judgment of the district court it had to file a cross-appeal attacking the judgment, which it did not do, and that not having done so it cannot urge the point in its brief in response to Bullard’s opening brief. But the union is not attacking the judgment, which dismissed the suit and so is just what the union wanted. The union is advancing an additional ground for that judgment. Appellees who were defendants in the district court — -that is, who are defending the dismissal of the action — will often add, to their arguments on the merits, jurisdictional arguments (failing to file administrative charges is a jurisdictional defect, as we shall see) for dismissal. See, e.g., DiLiberti v. United States, 817 F.2d 1259, 1262 (7th Cir.1987). It has never been thought that they must split the two types of argument and put the jurisdictional ones in a cross-appeal. What purpose would be served, except clutter? Cf. Jordan v. Duff & Phelps, Inc., 815 F.2d 429, 439 (7th Cir.1987).
The requirement of cross-appealing even in cases where the appellee is seeking to [468]*468alter the judgment has been vigorously attacked. See 15 Wright, Miller & Cooper, Federal Practice and Procedure § 3904, at pp. 418-19 (1976). It is by no means unwaveringly enforced, see id. at 416-18, and since we are obliged to consider jurisdictional issues whether or not they are raised, it can hardly matter that they were raised the wrong way. See id. at 417; Champagne v. Schlesinger, 506 F.2d 979, 982 (7th Cir.1974). Only we do not think they were raised the wrong way by being raised in the appellee’s responsive brief, for they are in defense of the judgment. It can make no difference, in an age that has turned its back on the technical niceties that so delighted earlier generations of lawyers, that if the appellee prevails on this ground we will be required to make a minor modification in the judgment, altering it from a judgment on the merits to a judgment on jurisdictional grounds. Such an alteration could make a difference in some cases, but not in this one, since Bul-lard cannot refile his claim.
So we cannot duck the jurisdictional issue on the ground that it should have been raised by way of cross-appeal; and let us turn to that issue. Title VIPs requirement that the plaintiff exhaust the administrative remedies provided by the statute is jurisdictional; that is, a court is obligated to enforce the requirement even if the defendant has overlooked it. This is not because requirements of exhausting administrative remedies are always jurisdictional; they are not, see, e.g., Granberry v. Greer, - U.S. -, 107 S.Ct. 1671, 95 L.Ed.2d 119 (1987); Kawitt v. United States, 842 F.2d 951, 953 (7th Cir.1988). But Title VII’s strong policy of encouraging conciliation, and of giving states that have anti-discrimination laws a chance to deal with discrimination before federal intervention, see 42 U.S.C. § 2000e-5(c); Martinez v. United Automobile, Aerospace & Agricultural Implement Workers, 772 F.2d 348, 350-51 (7th Cir.1985), argues for treating Title VIPs exhaustion requirements as jurisdictional. This conclusion is supported by dicta in many cases, see, e.g., McDonnell Douglas Corp. v. Green, supra, 411 U.S. at 798, 93 S.Ct. at 1822; Alexander v. Gardner-Denver Co., 415 U.S. 36, 47, 94 S.Ct. 1011, 1019, 39 L.Ed.2d 147 (1974); Choate v. Caterpillar Tractor Co., 402 F.2d 357, 359 (7th Cir.1968); Jones v. Truck Drivers Local Union No. 299, 748 F.2d 1083, 1086 (6th Cir.1984), and by this court’s holdings in several cases, see Bowe v. Colgate-Palmolive Co., 416 F.2d 711, 719 (7th Cir.1969); Williams v. General Foods Corp., 492 F.2d 399, 404-05 (7th Cir.1974); Eggleston v. Chicago Journeymen Plumbers’ Local Union No. 130, 657 F.2d 890, 905 (7th Cir.1981). The fact that Bullard filed an administrative charge against Sercon was not good enough. It did not give the union adequate notice that Bullard thought that it had discriminated against him in referrals, as distinct from Sercon’s having, discriminated against him in failing to reassign him after Lehner kicked him off the crew of the coke ovens. Compare id. at 905-08; EEOC v. Vucitech, 842 F.2d 936, 944 (7th Cir.1988).
The requirement of a timely filing is subject to the same defense of equitable tolling that a statute of limitations is subject to; it is a statute of limitations. Zipes v. Trans World Airlines, Inc., 455 U.S. 385, 393-98, 102 S.Ct. 1127, 1132-35, 71 L.Ed.2d 234 (1982). So a defendant who prevents the plaintiff from filing a timely administrative charge cannot turn around and demand that the action be dismissed because of that failure. See Janowiak v. Corporate City of South Bend, 750 F.2d 557, 561 (7th Cir.1984), vacated and remanded on other grounds, 107 S.Ct. 1620 (1987); Mull v. Arco Durethene Plastics, Inc., 784 F.2d 284, 291-93 (7th Cir.1986). The wrinkle here is that Bullard didn’t file an untimely administrative charge; he filed no charge. The availability of a defense of estoppel in such a case, although suggested by Jones v. Truck Drivers Local Union No. 299, supra, 748 F.2d at 1086, and EEOC v. Nevada Resort Ass’n, 792 F.2d 882, 887 (9th Cir.1986), and not necessarily excluded by our characterization of the requirement of filing an administrative charge as jurisdictional, seems dubious, to say the least. A person who has sued his employer can hardly argue that he was too intimidated to file [469]*469an administrative charge against the same employer.
At all events, Bullard’s defense must fail on its facts. He testified that Goin told him that if he sued the union he would never work in the construction industry again, but Goin testified that he said no such thing, and the district judge stated in his opinion that he believed Goin. By then the trial was over and the judge went on to decide the case on the merits in favor of the union. That was the wrong way to proceed. The judge should have held a hearing on the jurisdictional issue before the trial. Bullard and Goin would have testified and the judge would have decided whom he believed. If he believed Goin, as in the end he did, he would have dismissed the action against the union and saved himself and the parties the bother of a trial on the Title VII claim. In some cases a jurisdictional issue may be so entwined with the merits that it cannot feasibly or conveniently be resolved in a separate proceeding but must be deferred to trial, cf. Janowiak v. Corporate City of South Bend, supra, 750 F.2d at 561, but there is no indication that this was such a case. The judgment must therefore be modified to dismiss Bullard’s Title VII action against the union for lack of jurisdiction.
Our jurisdictional analysis, though unavoidable, is also to some extent a matter merely of shadow-boxing, for Bullard sued the union not only under Title VII but also under section 16 of the Civil Rights Act of 1870, now 42 U.S.C. § 1981 — a Reconstruction-era civil rights statute that, when employed as a vehicle for attacking employment discrimination, has been held to be substantively parallel to Title VII, see Hunter v. Allis-Chalmers Corp., 797 F.2d 1417, 1420 (7th Cir.1986), and that contains no requirement of exhausting administrative remedies. It is a nice question, which we shall elide, whether the claim is barred by the statute of limitations; for we do not think the judge’s determination that the union had not discriminated against Bullard was clearly erroneous. The essential question was whether Goin had stopped referring Bullard to jobs because Bullard had stopped paying his dues, as Goin testified, or because Bullard was black, as Bul-lard testified. This was a question of credibility, and as we noted earlier the trial judge’s credibility determinations are generally, and in this case, conclusive.
Modified and Affirmed.