A simple (deterministic) population dynamics model is used to examine the level of fishing mortality at which a population is expected to be driven to extinction (Fcrash). Values for Fcrash are determined for six marine fish species (Cape hake, blue grenadier, blue warehou, school shark, gummy shark, and orange roughy) subject to commercial harvest. The sensitivity of the value of Fcrash to changing the selectivity pattern of the fishery and the relationship between the size of the reproductive component of the population and subsequent births to allow for depensatory effects is examined. Fcrash is greatest for highly productive species and when the fishery does not target immature animals. The ratio of Fcrash to the fishing mortality at which maximum sustainable yield is achieved, FMSY, is a decreasing function of the productivity of the population. The possibility of depensation has little impact on FMSY but can substantially reduce the ratio Fcrash/FMSY. A series of stochastic simulations is conducted to assess the probability of detecting that the extent of fishing exceeds Fcrash using the current IUCN A criterion. The results of these simulations are also used to determine the probability that the IUCN A criteria will be triggered when fishing takes place at FMSY. The results indicate that there are substantial probabilities of incorrectly identifying species being harvested at FMSY as being threatened during the ‘fishing down’ phase and also of not identifying species actually at risk of extinction if fishing mortality is not reduced.