Phonological alternations are often specific to morphosyntactic context. For example, stress shift in English occurs in the presence of some suffixes, -al, but not others, -ing: "pa.rent, pa."ren.tal, "pa.ren.ting. In some cases a phonological process applies only in words of certain lexical categories. Previous theories have stipulated that such morphosyntactically conditioned phonology is word-bounded. In this paper we present a number of long-distance morphologically conditioned phonological effects, cases where phonological processes within one word are conditioned by another word or the presence of a morpheme in another word. We provide a model, Cophonologies by Phase, which extends Cophonology Theory, intended to capture word-internal and lexically specified phonological alternations, to cyclically generated syntactic constituents. We show that Cophonologies by Phase makes better predictions about the long-distance morphologically conditioned phonological effects we find across languages than previous frameworks. Furthermore, Cophonologies by Phase derives such effects without requiring the phonological component to directly reference syntactic features or structure.