Extensions to Categorial Grammars proposed to account for nonconstitutent conjunction and long-distance dependencies introduce the problem of equivalent derivations, an issue we have characterized as spurious ambiguity from the parsing perspective. In Wittenburg (1987) a proposal was made for compiling Categorial Grammars into predictive forms in order to solve the spurious ambiguity problem. This paper investigates formal properties o f grammars that use predictive versions of function composition. Among our results are (1) that grammars with predictive composition are in general equivalent to the originals if and only if a restriction on predictive rules is applied, (2) that modulo this restriction, the predictive grammars have indeed eliminated the problem of spurious ambiguity, and (3) that the issue o f equivalence is decidable, i.e., for any particular grammar, whether one needs to apply the restriction or not to ensure equivalence is a decidable question.