In local optionality, an optional process may apply at some loci in a form but not at others. Some theories of optionality, such as Partial Orders Theory, produce optionality by making multiple strict constraint rankings available, and have been claimed to be incompatible with local optionality: if the process-triggering constraint outranks faithfulness, the process applies exhaustively; under the opposite ranking, it applies nowhere. On this view, candidates in which the process applies at some loci but not others are harmonically bounded. This paper argues against that position by showing that for a variety of locally optional processes each locus can be independently manipulated if the theory makes use of constraints that target particular prosodic or morphosyntactic units – constraints that are motivated independently of their utility in local optionality. The result is that, contrary to the harmonic-bounding argument, Partial Orders Theory can provide plausible accounts of local optionality.