This paper describes and evaluates log-linear parsing models for Combinatory Categorial Grammar (CCG). A parallel implementation of the L-BFGS optimisation algorithm is described, which runs on a Beowulf cluster allowing the complete Penn Treebank to be used for estimation. We also develop a new efficient parsing algorithm for CCG which maximises expected recall of dependencies. We compare models which use all CCG derivations, including non-standard derivations, with normal-form models. The performances of the two models are comparable and the results are competitive with existing wide-coverage CCG parsers.