This article offers a critical conceptual discussion and refinement of Chomsky’s (2000, 2001, 2007, 2008) phase system, addressing many of the problematic aspects highlighted in the critique of Boeckx & Grohmann (2007) and seeking to resolve these issues, in particular the stipulative and arbitrary properties of phases and phase edges encoded in the (various versions of the) Phase Impenetrability Condition (PIC). Chomsky’s (2000) original conception of phases as lexical subarrays is demonstrated to derive these properties straightforwardly once a single assumption about the pairwise composition of phases is made, and the PIC is reduced to its necessary core under the Strong Minimalist Thesis (SMT)—namely, the provision of an edge. Finally, a comparison is undertaken of the lexical-subarray conception of phases with the feature-inheritance system of Chomsky 2007, 2008, in which phases are simply the locus of uninterpretable features (probes). Both conceptions are argued to conform to the SMT, and both converge on a pairwise composition of phases. However, the two conceptions of phases are argued to be mutually incompatible in numerous fundamental ways, with no current prospect of unification. The lexical-subarray conception of phases is then to be preferred on grounds of greater empirical adequacy.