This paper develops an analysis of sequential voicing in complex compounds. Left-branching and right-branching compounds exhibit a sharp contrast in sequential voicing, a contrast that calls for an analysis sensitive to compound-internal structure. This paper proposes an account couched in the Lexical Phonology-Morphology version of OT (LPM-OT). Compounding and sequential voicing occur alternately. As a result, this serial approach is necessarily sensitive to compound-internal structure. One more crucial analytical ingredient is covert voicing features. A covert voicing feature inserted in a previous cycle blocks sequential voicing. The proposed analysis is very similar to Ito & Mester's (1986) rule-based analysis, but there is an empirical reason for favoring the constraint-based approach. Other OT analyses, parallel and serial, are conceivable, but they make erroneous empirical predictions. The LPM-OT account is superior to them on empirical grounds.