Abkhaz’s lexical stress system uses an algorithm first stated by Dybo 1977 which gives word stress to the leftmost accented syllable not followed by another accented syllable. This has found expression in derivationalist frameworks in terms of an iterative left-to-right deletion of stress clash. Optimality Theory does not permit such processes. After surveying the facts of the language and reviewing Alderete 1999’s useful framework for analyzing cyclic stress effects in OT, the paper attempts systematically to check alternative venues for an analysis of these Abkhaz stress facts. In the end, none is found. Abkhaz joins Itelmen (Bobaljik 1997) in the file of “problem languages” for OT theories of stress.