The ranges of flow for which flames can stably be burnt in combustors based on extensive heat recirculation between products and reactants are examined in terms of the heat exchanger characteristics. This is important because, no matter how desirable it may be to burn poor fuels and mixtures of very low heat content efficiently, there are many applications for which the scheme would be attractive only for reasonably large throughputs and rates of energy release. A simple general theory based on the observed constant reaction temperature is shown to predict correctly the shape of the empirical curves for mixtures outside the flammability limits. Numerical correlations are obtained for a more detailed analysis of the very efficient double-spiral geometry. The results are compared with the theoretical maximum heat release rates per unit volume of flames in normally flammable mixtures. It is shown that mixtures containing only one fifth of the heat content at the normal limit of flammability in practice yield heat release rates comparable to the theoretical maximum for normal flames within the flammable range; the theoretical maximum for stoichiometric methane-air mixture should be attainable at little more than half the limit of flammability.