In this paper, I defend the hypothesis that each prepositional adverb in Modern German is formed from an adverb and a preposition – and not from two adverbs, as recently suggested in the literature. As major support for this hypothesis, I show on the example of darunter that the intensions of the lexical meanings of non-idiomatic prepositional adverbs are compositionally built from the intensions of preposition meanings by combining them in an appropriate way with the intension of an adverb meaning. The proposed analysis, formulated within the general framework of Integrational Linguistics (IL), also provides a solution for the animacy problem of prepositional adverbs, i.e. the problem that many prepositional adverbs in Modern German do not phorically take up animated entities, in particular, persons. This restriction follows, it is argued, from a sortal restriction inherited from the preposition meaning. While syntactic semantics can accommodate preposition meanings in order to properly relate preposition complement interpretations, there is no such accommodation in the case of prepositional adverbs, their valence being lexically reduced by one.