In Dutch V-final clauses the verbs tend to form a cluster in which the main verb is separated from its syntactic arguments by one or more other verbs. In HPSG the link between the main verb and its arguments is canonically modeled in terms of argument inheritance, also known as argument composition or generalized raising. When applied to Dutch, this treatment yields a number of problems, making incorrect predictions about the interaction with the binding principles and the passive lexical rule. To repair them this paper proposes an alternative, in which subject raising and complement raising are modeled in terms of different devices. More specifically, while subject raising is modeled in terms of lexical constraints, as for English, complement raising is modeled in terms of a more general constraint on headed phrases. This new constraint not only accounts for complement raising out of verbal complements, it also deals with complement raising out of adjectival and adpositional complements, as well as with complement raising out of PP adjuncts and subject NPs. It is, hence, a rather powerful device. To prevent overgeneration we add a number of constraints. For Dutch, the relevant constraints block complement raising out of CPs, V-initial VPs and P-initial PPs. For English, the Empty COMPS Constraint is sufficient to block complement raising entirely.