Caribbean coral reefs are widely thought to exhibit two alternate stable states with one being dominated by coral and the other by macroalgae. However, the observation of linear empirical relationships among grazing, algal cover and coral recruitment has led the existence of alternate stable states to be questioned; are reefs simply exhibiting a continuous phase shift in response to grazing or are the alternate states robust to certain changes in grazing? Here, a model of a Caribbean forereef is used to reconcile the existence of two stable community states with common empirical observations. Coral-depauperate and coral-dominated reef states are predicted to be stable on equilibrial time scales of decades to centuries and their emergence depends on the presence or absence of a bottleneck in coral recruitment, which is determined by threshold levels of grazing intensity and other process variables. Under certain physical and biological conditions, corals can be persistently depleted even while increases in grazing reduce macroalgal cover and enhance coral recruitment; only once levels of recruitment becomes sufficient to overwhelm the population bottleneck will the coral-dominated state begin to emerge. Therefore, modest increases in grazing will not necessarily allow coral populations to recover, whereas large increases, such as those associated with recovery of the urchin Diadema antillarum, are likely to exceed threshold levels of grazing intensity and set a trajectory of coral recovery. The postulated existence of alternate stable states is consistent with field observations of linear relationships between grazing, algal cover and coral recruitment when coral cover is low and algal exclusion when coral cover is high. The term ‘macroalgal dominated’ is potentially misleading because the coral-depauperate state can be associated with various levels of macroalgal cover. The term ‘coral depauperate’ is preferable to ‘macroalgal dominated’ when describing alternate states of Caribbean reefs.