Indexed constraints are often used in constraint-based phonological frameworks to account for exceptions to generalizations. A point of contention in the literature on constraint indexation revolves around indexed markedness constraints. While some researchers argue that only faithfulness constraints should be indexed, others argue that markedness constraints should be eligible for indexation as well. This article presents data from Japanese for which a complete synchronic analysis requires indexed markedness constraints but argues that such constraints are only necessary in cases where a phonological repair applies across a morpheme boundary. We then demonstrate that algorithms for learning grammars with indexed constraints can be augmented with a bias towards faithfulness indexation and discuss the advantages of incorporating such a bias, as well as its implications for the debate over the permissibility of indexed markedness constraints.