Pulse repetition frequency (PRF) staggering is a well-established technique in the pulse-Doppler radar, used in order to increase the unambiguous range and Doppler and to minimise blind spots. The study offers a new staggering dimension that can increase the number of different staggering choices. The new approach is to add an inter-pulse coherent phase-coded overlay. The code is shorter than the number of pulses in each PRF batch and is repeated an integer number of times within the batch. A required property of the phase code is perfect periodic autocorrelation, namely zero autocorrelation sidelobes. In order to minimise the added complexity, the overlay codes use a two-phase or three-phase alphabet. As in a conventional PRF staggering, there are P coherent batches, each using a different PRF, with its matched phase-coded overlay. The performance analysis uses a conventional binary integration rule that declares detection if there were H, or more, individual detections in the P batches.