An embodiment of this invention combines feed-forward and feedback frequency division circuits in a such a way, to provide greater flexibility in choosing the non-integer division ratios at the output, with little added complexity. Alternate embodiments include additional divider(s) in signal or feedback paths providing additional flexibility and design simplification. An embodiment uses in-phase/quadrature signals to select the desired modes at feedback-path and signal-path mixers. Various alternatives are also described.