Method, systems, and circuitries are provided for generating an output signal with reduced spurs by dithering. A method to generate an output signal having a desired frequency based on a reference signal having a reference frequency includes receiving a desired phase shift between a next cycle of the output signal with respect to a next cycle of the reference signal. A mapping between respective code words and phase shifts is read. A first codeword mapped to a first phase shift that is lower in value to the desired phase shift is identified. A second codeword mapped to a second phase shift that is higher in value to the desired phase shift is identified. The method includes selecting either the first codeword or the second codeword and generating the output signal based on the selected codeword.