Traditional autosegmental accounts of tone mapping invoke three independent factors: morphological category, tone quality, and a phonological directionality parameter. This article argues that the evidence for phonological directionality must be reconsidered. The article introduces a theory of Optimal Tone Mapping, in which attested patterns derive solely from the interaction of morphological directionality with quality-sensitive markedness constraints. The more restrictive theory of tone association that results from eliminating constraints that impose phonological directionality provides a new typology of tone melody languages.