Optimizing the bias modulation of a fiber-optic gyroscope is crucial to improving its precision. In this study, we propose and demonstrate the use of multiple harmonics of sinusoidal modulation as an intermediate alternative to the widely used modulation methods: sinusoidal and square-wave modulation. We show that this alternative integrates the advantages of each modulation method by providing a smooth modulation that produces a clean, spike-free output and a satisfactory signal-to-noise ratio. By using three harmonics of modulation in combination with a high frequency to reduce thermal phase noise, we obtained an angular random walk of5.2(2)μdeg/hand a bias instability of∼10μdeg/h. This is the highest performance ever reported for fiber-optic gyroscopes.