Late Visean (Asbian–Brigantian) platform carbonates in the British Isles show a pronounced cyclicity marked by the alternation of mainly subtidal carbonates and subaerial exposure surfaces. Whereas the cyclicity of shallow-water limestones of this age has been well-documented, there has been little attempt to understand the controls on larger-scale patterns such as those recognized in Pennsylvanian successions in the U.S.A. The principal aim of this study is to test two contrasting theories of cycle stacking via numerical forward modelling. Earlier studies of Pennsylvanian-early Permian platform carbonates in south-west U.S.A. suggest that cycle stacking patterns were controlled by the interaction of third- and fourth-order sea-level oscillations, with relatively uniform fourth-order oscillations altered mainly by the harmonic effect of lower-order sea-level changes. An alternative model is based on an insolation curve for the Carboniferous calculated using Milankovitch parameters. This model predicts a considerable variability in levels of solar insolation that would have affected the amplitude of fourth-order sea-level changes and cycle composition. Both of these ideas were examined via numerous model runs using CARBONATE 6.0 and a new program, CARBOSMUT. Model results were evaluated through the use of 3 key criteria derived from well-documented outcropping stratigraphies in the U.K.: (1) cycle stacking patterns and the stratigraphic position of major transgressions, (2) stratigraphic position of major faunal changes, (3) degree of development of subaerial exposure surfaces. Computer simulations and comparison with outcrop data suggest that a model invoking the interaction of relatively uniform fourth- (c.100 Kyr) and third-order sea-level oscillations is most appropriate for much of the late Visean, with major lowstands occurring at the mid-Asbian and Asbian–Brigantian boundary. Late Visean cycles are important exploration targets in the Pri-Caspian Basin, Kazakhstan and understanding the controls on stratal patterns is important as a potential exploration tool.