The observation that shallow-marine carbonate strata often have exponential lithofacies thickness distributions is one of the most fundamental results in carbonate stratigraphy in recent years because it is an observation that can be tested for its repeatability in various outcrop and subsurface examples, and also because it raises the question of what sedimentary processes and climatic and oceanographic settings might lead to formation of a particular lithofacies thickness distribution. This observation, in turn, links to the significant issue of how carbonate strata record climatic and oceanographic change through geological time. This study applies a simple one-dimensional numerical stratigraphic forward model of carbonate platform strata (Dougal) to study how relative sea-level oscillations could control lithofacies distribution. Dougal records platform-top carbonate accumulation influenced by water-depth dependent sediment production in euphotic, oligophotic and aphotic production profiles with a lag-depth controlling onset of production. Results from five single model runs highlight the issue of non-stationary behaviour where statistical properties of the strata change with elevation up the section, and show that exponential lithofacies thickness distributions can be generated from an entirely deterministic model. Results of multiple model runs, 27 200 in total, spanning a range of production and accommodation creation rates, demonstrate that the three main controls on carbonate lithofacies distribution in this one-dimensional model are: (i) complex variations in the rate of creation of accommodation, here due to high-frequency glacio-eustatic oscillations; (ii) rate of sediment production, dominated in these model runs by euphotic production rates; and (iii) operation of autocyclic oscillations in deposition driven by a lag-depth effect and formed during certain high-frequency rising limbs on the glacio-eustatic curve. In these multiple model runs, only ca 13% of the total runs created exponential distributions, compared with 28% in the documented outcrop examples, suggesting that other processes not included in this model play an important role. More work is required to determine what these processes might be. Obvious candidates would be the various sedimentary processes that occur in three dimensions on platform tops, such as sediment transport and variations in rate and type of sediment production related to biological variability, and other process that occur in other different depositional settings, for example sediment transport on slopes.