This paper defines a subregular class of functions called the tier-based synchronized strictly local (TSSL) functions. These functions are similar to the the tier-based input-output strictly local (TIOSL) functions, except that the locality condition is enforced not on the input and output streams, but on the computation history of the minimal subsequential finite-state transducer. We show that TSSL functions naturally describe rhythmic syncope while TIOSL functions cannot, and we argue that TSSL functions provide a more restricted characterization of rhythmic syncope than existing treatments within Optimality Theory.