  We consider dimensional crossover for an O(N) model on a d-dimensional
layered geometry of thickness L, in the sigma-model limit, using
``environmentally friendly'' renormalization. We show how to derive critical
temperature shifts, giving explicit results to one loop. We also obtain
expressions for the effective critical exponents delta and beta effective that
interpolate between their characteristic fixed point values assocliated with a
d and (d-1)-dimensional system in the limits T -> T_c(L), with
L(T-T_c(L))^{\nu}->infty, and T->T_c(L) for L fixed respectively, where T_c(L)
is the L-dependent critical temperature of the system.
