The electrostatic potential jump across fast-mode collisionless shocks is examined by comparing published observations, hybrid simulations, and a simple model in order to better characterize its dependence on the various shock parameters. In all three, it is assumed that the electrons can be described by an isotropic power law equation of state. The observations show that the cross-shock potential jump correlates well with the shock strength but shows very little correlation with other shock parameters. Assuming that the electrons obey an isotropic power law equation of state, the correlation of the potential jump with the shock strength follows naturally from the increased shock compression (Δn) and an apparent dependence of the power law exponent on the Mach number which the observations, indicate. We find that including a Mach number dependence for the power law exponent in the electron equation of state in our simple model, as suggested by the observations, produces a potential jump which better fits the observations. On the basis of the simulation results and theoretical estimates of the cross-shock potential, we also discuss how the cross-shock potential might be expected to depend on the other shock parameters, namely, &bgr;e, and &thgr;Bn. Given the broad range of parameters lumped together in the observational results, we feel that the qualitative agreement between them and the simulations is quite good and can be used to better elucidate the nature of the discrepancies. ¿American Geophysical Union 1991