In this paper we study the complexity of Bounded Color Multiplicity Graph Isomorphism BCGIb: the input is a pair of vertex-colored graphs such that the number of vertices of a given color in an input graph is bounded by b. We show that BCGIb is in the #L hierarchy (more precisely, the ModkL hierarchy for some constant k depending on b). Combined with the fact that Bounded Color Multiplicity Graph Isomorphism is logspace many-one hard for every set in the Modk L hierarchy for any constant k, we get a tight classification of the problem using logspace-bounded counting classes. © 2005 IEEE.