Zipser's (1986) formulation of the beta model for navigation suffers from two major drawbacks; it requires a minimum of three landmarks, and that each landmark's position relative to the current position be accurately estimated. This paper extends the beta model by demonstrating that it can apply in the two landmark case, and also when one of the two landmarks is too distant for its coordinates to be estimated with any accuracy. This enables the model to meet some of the criteria for a successful account of navigation in the rat and the gerbil.