Linguistic phylogenies are commonly inferred from abstract cognate classifications that encode relationships among lexemes. Although widespread, this practice has well-recognized limitations: it discards the phylogenetic signal contained in segmental word forms; restricts the range of evolutionary questions that can be addressed; and treats cognacy judgments, which are hypotheses, as observed data. We introduce a comparative framework that addresses these limitations by modeling the evolution of aligned cognate word forms directly. Our approach adapts the TKF91 model of molecular evolution, originally developed to account for insertion and deletion events in DNA sequences, to the domain of linguistic data. By operating on segmental strings rather than abstract character codings, the framework enables phylogenetic inference from observable word forms and supports quantitative investigation of sound change. We demonstrate its utility through analyses that illuminate patterns of segmental stability and the evolution of phonological inventories.