Source-side reordering has recently seen a surge in popularity in machine translation research, often providing enormous reductions in translation time and showing good empirical results in translation quality. For many language pairs, however--especially for translation into morphologically rich languages--the assumptions of these models may be too crude. But while such language pairs call for more complex models, these could increase the search space to an extent that would diminish their benefits. In this paper, we examine the question whether purely syntax-oriented adaptation models (i.e., models only considering word order) can be used as a means to delimit the search space for more complex morphosyntactic models. We propose a model based on a popular preordering algorithm (Lerner and Petrov, 2013). This novel preordering model is able to produce both n-best word order predictions as well as distributions over possible word order choices in the form of a lattice and is therefore a good fit for use by richer models taking into account aspects of both syntax and morphology. We show that the integration of non-local language model features can be beneficial for the model's preordering quality and evaluate the space of potential word order choices the model produces.