The extinction of contextual fear is commonly an essential requirement for successful exposure therapy for fear disorders. However, experimental work on extinction of contextual fear is limited, and there little or no directly relevant theoretical work. Here, we extend BACON, a neurocomputational model of context fear conditioning that provides plausible explanations for a number of aspects of context fear conditioning, to deal with extinction (calling the model BaconX). In this model, contextual representations are formed in the hippocampus and association of fear to them occurs in the amygdala. Representation creation, conditionability, and development of between-session extinction are controlled by degree of confidence (assessed by the Bayesian weight of evidence) that an active contextual representation is in fact that of the current context (i.e., is "valid"). The model predicts that: (1) extinction which persists between sessions will occur only if at a sessions end there is high confidence that the active representation is valid. It follows that the shorter the context placement-to-US (shock) interval ("PSI") and the less is therefore learned about context, the longer extinction sessions must be for enduring extinction to occur, while too short PSIs will preclude successful extinction. (2) Short-PSI deficits can be rescued by contextual exposure even after conditioning has occurred. (3) Learning to discriminate well between a conditioned and similar safe context requires representations of each to form, which may not occur if PSI was too short. (4) Extinction-causing inhibition must be applied downstream of the conditioning locus for reasonable generalization properties to be generated. (5) Context change tends to cause return of extinguished contextual fear. (6). Extinction carried out in the conditioning context generalizes better than extinction executed in contexts to which fear has generalized (as done in exposure therapy). (7) BaconX suggests novel approaches to exposure therapy.