The paper considers a novel technique for the measurement and correction of the Doppler shift (frequency offset) in a received QPSK signal, where the Doppler shift may be very high, the signal/noise ratio very low, and the receiver has no prior knowledge of the received data symbols. The technique is designed for synchronous data and is to operate prior to the instigation of a phase locking algorithm necessary for coherent demodulation. It reduces the Doppler shift to a value within the capture range of the phase correction loop, and does not operate during the phase acquisition period nor during data detection. The residual Doppler shift in the coherently demodulated baseband signal at the receiver is measured by correlating this signal with two components (complex exponentials) of equal frequency but one positive and the other negative, where the frequency is an appropriate fraction (typically around one half) of the highest frequency component of the baseband signal. Depending on which of the two correlators gives the greater output signal, the frequency of the reference carriers in the coherent demodulator is increased or decreased to reduce the residual Doppler shift in the demodulated baseband signal. The paper first describes various arrangements of the new Doppler-shift corrector, together with the original DFT Doppler-shift corrector, from which these have been derived, and it then presents the results of computer-simulation tests to assess the performances of the different systems.