A semiconductor-based Mach-Zehnder modulator (MZM) is configured for push-pull bias dithering to control the MZM bias at a desired set point. When two such MZM modulators are connected in parallel to form an IQ modulator, bias settings for both MZMs and the IQ bias may be controlled from an output of the IQ modulator to minimize both the IQ offset and the quadrature error of the output signal constellation even for non-ideal MZMs with low extinction ratios.