In this paper we address the case assignment properties of (spatial) prepositions in German. Applying a word-syntactic framework in the spirit of Distributed Morphology (Halle & Marantz 1993), we offer a post-syntactic approach to morphological case (Marantz 1991) in German PPs. We argue that dative is the case that is inherently assigned by the category P and that other cases are derived by regular (Path Impoverishment) or idiosyncratic morphological operations. In particular, we implement the well-known dative/accusative alternation in German PPs that reflects a semantic alternation between a locative and a directional meaning. We also address those spatial prepositions that invariantly combine with a particular case like route prepositions (with accusative) and inherently directional prepositions (with dative). Our analysis turns out to be superior to lexicalist approaches such as Bierwisch (1988) in that we can model the ambiguous preposition über ('above', 'over', 'across') with one underlying element, while in lexicalist approaches one arguably has to postulate two independent lexical entries.