A data-directed frequency-and-phase lock loop for an offset-QAM modulated signal comprises a first multiplier that multiplies the signal by the output of a VCO. The output of the first multiplier is phase-shifted by a second multiplier, then convolved by a third multiplier. The output of the third multiplier is split, with each portion being passed through a frequency-shift multiplier and a frequency-and-phase lock loop. The output of the two frequency-and-phase lock loops is summed and returned to the VCO to complete the feedback loop.