An idea used by Thieme (J. Math. Biol. 8, 173-187, 1979) is extended to show that a class of integro-difference models for a periodically varying habitat has a spreading speed and a formula for it, even when the recruitment function R(u, x) is not nondecreasing in u, so that overcompensation occurs. Numerical simulations illustrate the behavior of solutions of the recursion whose initial values vanish outside a bounded set.