In this paper we provide an alternative to the generalized model of indivisible good allocation available in Sonmez [1991]. In this context we prove a theorem that gives sufficient conditions for an allocation rule to be weakly coalitionally strategy-proof. We also prove that with existence of a Pareto optimal allocation rule along with another condition introduced in this paper, is sufficient for essentially single-valued Pareto correspondence and hence is also sufficient for essentially single-valued core correspondence, in the presence of a mild domain assumption.