We present a model of the head-direction circuit in the rat that improves on earlier models in several respects. First, it provides an account of some of the unique characteristics of head-direction (HD) cell firing in the lateral mammillary nucleus and the anterior thalamus. Second, the model functions without making physiologically unrealistic assumptions. In particular, it implements attractor dynamics in postsubiculum and lateral mammillary nucleus without directionally tuned inhibitory neurons, which have never been observed in vivo, and it integrates angular velocity without the use of multiplicative synapses. The model allows us to examine the relationships among three HD areas and various properties of their representations. A surprising result is that certain combinations of purported HD cell properties are mutually incompatible, suggesting that the lateral mammillary nucleus may not be the primary source of head direction input to anterior thalamic HD cells.