A method, implementable in a resonator fiber optic gyroscope (RFOG) having a first wave generator configured to produce a first resonance-detection modulating signal at a fundamental resonance frequency, includes generating with at least a second wave generator a second modulating signal at an even harmonic of the first modulating signal. The second signal is amplitude-modulated (AM) at a frequency that is harmonically unrelated to the first signal. The first signal is added to the second signal with a summing element to produce a resonator output bias error signal. An optimum amplitude is determined from the error signal. Subsequently, the amplitude of the first signal is controlled to the optimum amplitude.