A mathematical model of carbonate platform evolution is presented in which depth-dependent carbonate growth rates determine platform-top accumulation patterns in response to rising relative sea-level. This model predicts that carbonate platform evolution is controlled primarily by the water depth and sediment accumulation rate conditions at the onset of relative sea-level rise. The long-standing ‘paradox of a drowned platform’ arose from the observation that maximum growth rate potentials of healthy platforms are faster than those of relative sea-level rise. The model presented here demonstrates that a carbonate platform could be drowned during a constant relative sea-level rise whose rate remains less than the maximum carbonate production potential. This scenario does not require environmental changes, such as increases in nutrient supply or siliciclastic sedimentation, to have taken place. A rate of relative sea-level rise that is higher than the carbonate accumulation rate at the initial water depth is the only necessary condition to cause continuous negative feedbacks to the sediment accumulation rates. Under these conditions, the top of the carbonate platform gradually deepens until it is below the active photic zone and drowns despite the strong maximum growth potential of the carbonate production factory. This result effectively resolves the paradox of a drowned carbonate platform. Test modelling runs conducted with 2·5 m and 15 m initial sea water depths at bracketed rates of relative sea-level rise have determined how fast the system catches up and maintains the ‘keep-up’ phase. This is the measure of time necessary for the basin to respond fully to external forcing mechanisms. The duration of the ‘catch-up’ phase of platform response (termed ‘carbonate response time’) scales with the initial sea water depth and the platform-top aggradation rate. The catch-up duration can be significantly elongated with an increase in the rate of relative sea-level rise. The transition from the catch-up to the keep-up phases can also be delayed by a time interval associated with ecological re-establishment after platform flooding. The carbonate model here employs a logistical equation to model the colonization of carbonate-producing marine organisms and captures the initial time interval for full ecological re-establishment. This mechanism prevents the full extent of carbonate production to be achieved at the incipient stage of relative sea-level rise. The increase in delay time due to the carbonate response time and self-organized processes associated with biological colonization increase the chances for platform drowning due to deepening of water depth (> ca 10 m). Furthermore this implies a greater likelihood for an autogenic origin for high-frequency cyclic strata than has been estimated previously.