Motivated by the phenomena that occur at the ablation front of a laser-driven target, a theory of the convective stabilization of the Rayleigh-Taylor instability is derived which is applicable for wavelengths that are long compared with the density-gradient scale length. Thermal conduction processes are not treated. The system of linearized equations is closed by assuming that the density jump is some unspecified function of the hydrodynamic and transport variables and linearizing this relationship. The resulting growth rates are closer to those given by the Takabe formula than the results of previous analytical theories that include convection but neglect thermal conduction.