Case assignment and argument licensing in process nominals, that is, nouns such as destruction that are morphologically related to verbs, are assumed to operate in a verblike manner both within government-and-binding theory and, more recently, within the distributed morphology framework. The data from Russian challenge this approach and reveal that there is an important difference between the verbal and the nominal domains: case assignment in verbs is sensitive to the underlying argument structure, but in nominals to surface structure, that is, the collection of overt arguments. We propose a hierarchy of case-assignment rules that applies in the nominal domain. Moreover, within the nominal domain, case assignment is uniform: the same rules apply to different types of nominals, including prototypical process nominals and relational nouns. The main theoretical advantage of our lexicalist, constraint-based approach is that it can capture similarities between the verbal and the nominal domains, seen in the assignment of inherent and lexical cases, but also in their fundamental differences.