Theoretical interpretations are reviewed and discussed for recent experimental observations on the pressure dependence of nonmetalized hybrid fuel regression rates. It is emphasized that regression rate data alone are not likely to be capable of demonstrating whether the major heat-release reactions are heterogeneous or homogeneous. A method for plotting experimental data is suggested which, in principle, can distinguish between rival qualitative homogeneous-reaction theories, one of which is developed herein. It is shown that existing data are not sufficiently accurate to distinguish between alternative homogeneous-reaction hypotheses, and the need (and feasibility) of developing an accurate homogeneous-reaction theory that describes small departures from pressure independence is underscored. On the basis of an approximate homogeneous-reaction analysis of large departures from pressure independence (which shows that the regression rate varies as the square root of the pressure if it is assumed that the fuel concentration at the wall is independent of pressure), it is concluded that many difficulties will arise in attempts to predict theoretical values for homogeneously controlled regression rates in the strongly pressure-dependent regime.