In morphologically rich languages, should morphological and syntactic disambiguation be treated sequentially or as a single problem? We describe several efficient, probabilisticallyinterpretable ways to apply joint inference to morphological and syntactic disambiguation using lattice parsing. Joint inference is shown to compare favorably to pipeline parsing methods across a variety of component models. State-of-the-art performance on Hebrew Treebank parsing is demonstrated using the new method. The benefits of joint inference are modest with the current component models, but appear to increase as components themselves improve. 1