Joint morphological and syntactic analysis has been proposed as a way of improving parsing accuracy for richly inflected languages. Starting from a transition-based model for joint part-of-speech tagging and dependency parsing, we explore different ways of integrating morphological features into the model. We also investigate the use of rule-based morphological analyzers to provide hard or soft lexical constraints and the use of word clusters to tackle the sparsity of lexical features. Evaluation on five morphologically rich languages (Czech, Finnish, German, Hungarian, and Russian) shows consistent improvements in both morphological and syntactic accuracy for joint prediction over a pipeline model, with further improvements thanks to lexical constraints and word clusters. The final results improve the state of the art in dependency parsing for all languages.