Anti-pied-piping is a widespread but understudied phenomenon where a language targets a proper subpart of the logical focus for focus morphosyntax: for example, focus particle placement or focus movement. We show that anti-pied-piping is attested in over 60 languages from over 40 distinct language groups. We present a theory of focus particle syntax/semantics that involves severing the pronounced position of a focus particle and the logical position of its corresponding semantic contribution, which successfully accounts for both anti-pied-piping and pied-piping behavior. Constraints on attested anti-pied-piping behavior and its interaction with movement show that particle placement takes place at particular, punctuated points in the derivation, in a cyclic model of syntactic structure-building. We also discuss the relation of particle placement to other processes such as stress assignment.