In the generative tradition, Accusative case ACC is often analyzed as a dependent Case, where being dependent means being dependent on another argument (Burzio 1986), more precisely a theta-role, or being dependent on a chain assigning Nominative case NOM to another argument (Marantz 1991), more precisely, an unmarked, i.e. non-lexically governed, case. In both approaches, ACC is a result of grammatical competition. The Minimalist Program (Chomsky 2001, 2008) seems to be an exception: in this framework, abstract Case is assigned by functional heads. Concretely, ACC is assigned by v*. Whether or not v* assigns ACC then depends on whether or not v* is a strong phase. Even though the Minimalist Program doesn't seem to employ a competition view of ACC as a dependent case, it is at its core a look-ahead system. Although the dependency on another argument is not explicitly declared, it is inherent to the system. This paper presents data from Polish, Ukrainian and Northern Russian that contradict the dependency view of ACC and suggest an alternative in terms of structure-dependency, independent of another argument receiving a theta-role or another case being assigned to a chain. This bears on the question of the role of case in syntax and on the nature of spell-out and of cyclic domains.