An improved, induced-draft, gas-fired furnace which is adapted to operate at any of a high, medium and low firing rate. A pressure sensing assembly generates differential pressure signals that vary in accordance with the pressure across a heat exchanger assembly. A gas flow control assembly is responsive to the differential pressure signals, and to signals received from the furnace control circuit, to supply gas to the furnace at any of its three different firing rates, the lowest of those said firing rates corresponding to a gas-air mixture which cannot be ignited. The furnace control circuit applies to the circulating air blower, and to the inducer blower, speed controls signals that are so related to one another that the fuel utilization efficiency of the furnace is at least as great during steady state operation at its low firing rate as during steady state operation at its medium firing rate.