Significance Maintaining robust circadian rhythms has been linked to longevity and metabolic health. Because these rhythms are disturbed by factors such as jet lag, shift work, and high-fat diets, there is interest in developing pharmacological control strategies to modulate circadian function. The design of therapeutic strategies is currently limited by the lack of a clear mechanistic understanding of interactions between posttranslational regulators, as efficient control of clock behavior will likely require several simultaneous modulations. Here we show fundamentally different clock responses from the manipulation of two clock regulators previously thought to act via similar mechanisms. Using mathematical modeling, we provide a mechanistic interpretation for the relationship between these two regulators, lending insight into circadian regulation and potential pharmacological control.