Tabulation of thickness data on nearly 3000 Proterozoic and Paleozoic peritidal carbonate cycles indicates that metre-scale facies associations exhibit exponential thickness frequency distributions. Because carbonate deposition occurs during infilling of available space between sea level and the surface of the preceding cycle, and because the rate of generation of accommodation space is ultimately determined by rates of platform subsidence, thicknesses of individual cycles must record the duration of time since deposition of underlying units. Exponential thickness distributions therefore require either that upward-shoaling carbonates record aperiodic accumulation, or that any periodic forcing manifest during sedimentation has been masked by the vagarious nature of depositional processes. Such a conclusion is contrary to interpretation of such carbonate units as originating from high-frequency eustatic change. In addition, exponential thickness distributions and sequence thickness structures are replicated when assuming a random probability of carbonate deposition under conditions of constant subsidence. The nature of cycle thickness distributions therefore invalidates virtually any endeavor to derive an average depositional period from mean cycle thicknesses, and refutes the use of such estimates as proxy records of past sea-level oscillation frequency, whether they are related to Milankovitch-band climate forcing or to any other periodic process.