Up until about five years ago all models for hard X-ray bursts consisted of streaming nonthermal electrons interacting with an ambient plasma (Brown 1975). Even in its most efficient form of thick-target emission in which electrons are stopped in the ambient plasma, this type of model is very inefficient because the electrons lose about 105 times more energy in Coulomb collisions with the ambient plasma than in X-rays resulting from bremsstrahlung. As a result, according to the latest estimates, at least 20% of the dissipated flare energy must go into accelerated electrons at the peak of the impulsive phase (Duijveman et al. 1982). Stimulated by observations of hard X-rays with thermal spectra (Crannel et al. 1978; Elcan 1978), analysis of a thermal model in which all the electrons in a given volume are heated to a temperature Te = 108K was begun (Brown et al. 1979; Smith and Lilliequist 1979; Vlahos and Papadopoulos 1979). It was recognized from the beginning that some electrons in the tail of the distribution would escape through the conduction fronts formed and mimic nonthermal streaming electrons. This thermal model with loss of electrons or dissipation became known as the dissipative thermal model (Emslie and Vlahos 1980). If the escaping electrons are not replenished, they will cease to make a contribution after a fraction of a second and the source will become a pure thermal source. It will be shown below that collisional replenishment (Smith and Brown 1980) is too slow.