Experiments show that the hysteresis of the bistable Belousov-Zhabotinsky reaction contracts along the directions of both the control parameter and the response variable as the stirring rate is decreased. A one-dimensional stochastic model reproduces qualitatively and quantitatively the effect of stirring on both steady states and hysteresis limits. The model suggests a classification of known stirring effects, A system behaves effectively one-dimensionally when its hysteresis contracts at low stirring. Otherwise, the system is described by at least two dynamical variables.