Let G be a profinite group, p a prime number and A a profinite (Z) over cap [G]-module of finite projective p-dimension (pd)G, p (A). Let N be a closed normal subgroup of G such that N is of finite cohomological p-dimension cd(p)(N), H-k(N, F-p) is nonzero and finite for k = min{cd(p)(N),pd(G,p)(A)} and N acts trivially on A. Then the virtual projective p-dimension vpd(G/N,p)(A) of A as a (Z) over cap [G/N]-module is finite and vpd(G/N,p) (A) = pd(G, p) (A) - k. In the case when A = (Z) over cap this generalizes the main result from [Th. Weigel, P.A. Zalesskii, Profinite groups of finite cohomological dimension, C. R. Acad. Sci. Paris Ser. I 338 (2004) 353-358]. (c) 2005 Elsevier Inc. All rights reserved.2952415425