Ran Levi Northwestern University (previous, University of Heidelberg) Let G be a finite p-superperfect group. A conjecture of F. Cohen suggests that \Omega BG^p is resolvable by finitely many fibrations over spheres and iterated loop spaces on spheres, where (-)^p denotes the p-completion functor of Bousfield and Kan. We produce a counter-example to this conjecture and discuss some related aspects of the homotopy type of \Omega BG^p. Appeared in Progress in Math. Vol 136, (1996) Birkhauser Verlag.