This paper is the second in a series of two papers presenting recent developments concerning the interaction between aspectual classes of predicates and the semantics of aspectual for-phrases. Aspectual for-phrases must modify predicates which are homogeneous - meaning that the predicate spreads appropriately to subintervals. For eventive predicates the relevant notion of homogeneity should be a dynamic notion - sensitive to the arrow of time. We present a recently developed semantic framework in which eventive predicates are incrementally homogeneous, meaning that the predicate characteristics are preserved for each event from its onset through all incremental development stages. We show how incremental homogeneity deals with the felicity facts concerning aspectual for-phrases, and discuss complex-activity forming operations which turn heterogeneous predicates into homogeneous ones, in particular, as triggered by bare arguments and by iteration.