Deflagrations in porous energetic materials under confinement are generally characterized by a relatively rapid increase in the burning rate as the pressure difference, or overpressure, in the burned-gas region relative to that deep within the pores of the unburned solid increases. Specifically, there appears to be a range of overpressures in which the sensitivity, or slope, of the propagation speed as a function of overpressure transitions from relatively small to large values. This effect has been qualitatively attributed to the fact that a sufficient overpressure reverses the gas flow and thus allows the burned gas to permeate, and therefore preheat, the porous material. However, quantitative descriptions of both the process itself and the corresponding burning-rate dependencies have only recently been achieved. The present work reflects a further refinement in this analytical description in that the melt layer, which underlies several previous studies and is likely to exist only at modest overpressures, is replaced by sublimation and pyrolysis at the material surface, followed by an attached gas flame that converts the unburned gaseous reactants to final products. As a result, gaseous reactants as well as products now permeate the porous solid, thereby affecting the propagation speed significantly and modifying both the combustion-wave structure and the transition to convection-enhanced burning.