This Selective Service case has returned to this court following remand for further testimony in the district court. Wallace v. United States, 403 U.S. 902 , 91 S.Ct. 2211 , 29 L.Ed.2d 678 (1971), vacating United States v. Wallace, 435 F.2d 12 (9th Cir. 1970).

In what he termed an “act of solidarity,” Wallace participated in a symbolic surrender of Selective Service cards in 1967. Shortly thereafter, his local board reviewed his classification and decided that Wallace was no longer eligible for an occupational deferment (Class II-A). Wallace and his employer filed timely appeals, but the appeal board upheld the determination of the local board.

Pursuant to the remand, the district court offered the government the opportunity to rebut the inference that Wallace had been deprived of the occupational deferment as a punitive measure discountenanced in Gutknecht v. United States, 396 U.S. 295 , 90 S.Ct. 506 , 24 L.Ed.2d 532 (1970).

The members of the appeal board had no recollection of the case independent of the Selective Service file. Wallace’s file contained a letter from the acting state director suggesting that the local board consider declaring Wallace and certain other registrants delinquents “by reason of their failure to have in their possession registration certificates and valid classification cards” and accelerating their induction into the armed forces.

In our previous opinion we held that procedural errors allegedly committed by the local board had been cured by the de novo review of the appeal board, but we did not consider the import of the acting director’s letter. See United States v. Wallace, supra. Where the record shows that the appeal board may have been guided by legally erroneous official recommendations, the government must prove that the proceedings were free from the taint of impropriety. Clay v. United States, 403 U.S. 698, 704 , 91 S.Ct. 2068 , 29 L.Ed.2d 810 (1971).

The testimony by the appeal-board members as to how they now think they would have reacted to Wallace’s file is inherently speculative. The danger of post hoc rationalization makes this kind of testimony little better than pure guesswork. Without definitive testimony as to what, in fact, did transpire when the appeal board convened to evaluate Wallace’s appeal, we are unable to say with the requisite certainty that the improper suggestion of the acting state director played no part in the appeal board’s deliberations. A proper concern for “the integrity of the Selective Service System,” 403 U.S. at 704 , 91 S.Ct. at 2072 , therefore requires reversal.

Reversed.