Data from the perfect in Classical Greek provide empirical evidence for inwardly-and outwardly-sensitive span-conditioned allomorphy and indicate the need for a post-Vocabulary Insertion linearization process. The data also support the extremely late computation of the phonology of reduplicants. Perfect aspect in Classical Greek is realized via three distinct exponents: a reduplicative prefix, a suffix -/k/ (for some verbs) or stem allomorphy (for others), and a dedicated set of agreement suffixes. I argue that this case of Multiple Exponence results from one direct exponent of the Aspect[perfect] head and two cases of allomorphy at other nodes conditioned by spans that include the Aspect[perfect] head. The reduplicant is a Vocabulary Item (RED) that instantiates Aspect. Its phonology is determined after both Vocabulary Insertion and linearization. The -/k/ suffix is an outwardly-sensitive allomorph of Voice[active] conditioned by the span ⟨Aspect, Tense⟩, and perfect stem allomorphy in verbs that show it is conditioned by ⟨Voice, Aspect, Tense⟩. The agreement suffixes are inwardlysensitive allomorphs conditioned by the span ⟨Voice, Aspect, Tense, Mood⟩. When taken together, the data indicate that Vocabulary Insertion must proceed cyclically, and that linearization must happen very late -after Vocabulary Insertion -since the realizations of both Voice[active] and AGR are conditioned by spans of hierarchically adjacent, rather than surface-contiguous, heads. The Greek data are essential for our understanding of the post-syntactic order of operations.