Carbonate lithofacies thickness distributions are of fundamental importance to understanding shallow-water carbonate deposystems because they record evidence of the lateral distribution and migration of lithofacies elements, as well as evidence for the various other intrinsic and extrinsic controls on stratal geometries and accumulation rates. Previous analyses of lithofacies thickness data led to the suggestion that exponential distributions are ubiquitous in the ancient record. This has been interpreted to indicate deposition by stochastic Poisson process lithofacies mosaics. To further investigate these ideas statistical analysis of 56 outcrop and core examples was performed. The Kolmogorov-Smirnov test was used to identify the degree to which measured lithofacies thicknesses are well represented by a theoretical exponential distribution. Results from this analysis show that 16 of the 56 examples can be confidently shown to be exponential, while 28 are very probably not exponential. This indicates that stochastic Poisson processes are a plausible explanation for many carbonate successions, but they do not explain all of those tested here, suggesting that other non-Poisson processes, either stochastic or deterministic in nature, or both, must also be important. Thus lithofacies planform geometries, and the processes controlling vertical stacking in ancient carbonate platform top deposystems, were likely more diverse than has been suggested, requiring significant further quantitative analysis and numerical forward modeling to properly understand.