Frequency-shift-keying (FSK) radars are used to measure the absolute range and radial speed of multiple moving targets with different velocities in short-range scenarios. The range is calculated from a well-known formula that depends on the phase difference of the in-phase/quadrature (I/Q) components associated with the two time-multiplexed transmitted tones. From a signal perspective, this work demonstrates that an additional novel term in the equation must be compensated to gain enhanced range accuracy in the measurements. This may facilitate the exploitation of longer waveform periods, leading to a relaxation in the stringent locking-time requirements currently imposed on the phase-locked loops of the signal-generation blocks in FSK radars. Moreover, detailed simulation examples for multiple moving targets are addressed. The obtained results validate the theoretical framework and the proposed computationally-efficient compensation algorithm for improved absolute-range-measurement accuracy in FSK radars.