A digital fuel control (53) for a helicopter engine (20) controls fuel flow (52) to the engine in response to a turbine reference speed (62) determined in a normal mode (Fig. 5) to be a rated speed, in a fade-in mode (Fig. 6) to be incremented (117, 120) to an estimated optimum minimum speed (114, 115, 125), in an optimizer mode (Fig. 7) to be incremented (138) in a direction (137) leading to least fuel consumption (135), and in a fade-out mode (Fig. 8) to be incremented (151, 153) back to rated speed (154). The invention provides an engine reference speed which results in minimum fuel consumption during cruise flight.