  If F is an infinitely differentiable function whose composition with a
blowing-up belongs to a Denjoy-Carleman class C_M (determined by a log convex
sequence M=(M_k)), then F, in general, belongs to a larger shifted class C_N,
where N_k = M_2k; i.e., there is a loss of regularity. We show that this loss
of regularity is sharp. In particular, loss of regularity of Denjoy-Carleman
classes is intrinsic to arguments involving resolution of singularities.
