When faced with complex phrasal phonological patterns, linguists are faced with a dilemma: since complex phenomena rarely lend themselves to simple analyses, where is the analytical complexity best justified? This talk explores the question using the test case of argument-head tone sandhi in Seenku (Western Mande, Burkina Faso), arguing that a morphological approach with a hierarchical lexicon offers a fuller account of the data than a complex phonological one. In Seenku, internal arguments trigger sandhi on their following heads. Like Taiwanese, tone changes are largely paradigmatic, but unlike most Sinitic sandhi systems, each base tone has more than one sandhi tone, depending on the argument's tone and whether it is pronominal or non-pronominal. A phonological account would necessitate mechanisms like anti-faithfulness or contrast preservation, but just a single underlying form could be maintained. A morphological account treats the alternations as allomorph selection, which requires a hierarchical lexicon with paradigms of subcategorization frames. Both approaches introduce complexity, but the phonological approach fails to account for several data patterns, including differences between pronominal and non-pronominal arguments, the immutability of multi-tonal heads, and lexical exceptions. Further, the single underlying form would be necessarily abstract, since certain heads appear obligatorily with an argument and hence always undergo sandhi. The allomorph selection approach addresses each of these complications and more naturally characterizes the linguistic competence of Seenku speakers. This result suggests that the lexicon may play a more powerful role than is often assumed, especially in cases where sound change has obscured once transparent phonological motivations.