1. Introduction. In this paper, we shall study cellular decompositions of 3-manifolds for which the associated decomposition space is also a 3-manifold. In [4], Bing raised the following question : Does each point-like decomposition of E3 yield E3 if it yields a 3-manifold ? This question can be generalized as follows : If a cellular decomposition of a 3-manifold M yields a 3-manifold N, then are M and N homeomorphic ? We shall establish conditions sufficient to insure that, under the hypothesis stated, M and N are homeomorphic.The main theorem of this paper can be stated as follows. Suppose that M is a connected 3-manifold and G is a cellular decomposition of M such that the associated decomposition space is a 3-manifold N. Let P denote the projection map from M onto N, and let HG denote the union of all the nondegenerate elements of G. Thus C\P [HG] is the set of singular points of the map P. Our main result then states that if N has a triangulation Jsuch that (1) no vertex of J belongs to Cl P[HG] and (2) for each 3-simplex a of T, P ~1 [