This paper compares a number of generative probability models for a wide-coverage Combinatory Categorial Grammar (CCG) parser. These models are trained and tested on a corpus obtained by translating the Penn Treebank trees into CCG normal-form derivations. According to an evaluation of unlabeled word-word dependencies, our best model achieves a performance of 89.9%, comparable to the figures given by Collins (1999) for a linguistically less expressive grammar. In contrast to Gildea (2001), we find a significant improvement from modeling word-word dependencies.