Idle speed stability is imparted to a compression ignition engine by processing data values for actual engine speed and desired engine speed to yield a data value for engine speed error; processing (22) the data value for engine speed error according to a governor algorithm for yielding a data value for a mass fuel rate for governed fueling of the engine; c) processing (24) the data value for mass fuel rate for governed fueling of the engine and the data value for actual engine speed to yield a data value for a quantity of fuel to be injected into an engine cylinder during an ensuing stroke of a piston within the cylinder; and d) injecting (30) that quantity of fuel into the cylinder during that stroke.