This work examines time and frequency domain implementations for estimating delays between acoustic signals arriving at spatially distributed microphones. A parametric variant of the phase-only transform (PHAT) is introduced for partially whitening the signal before estimating the delay. The PHAT variant is referred to as the PHAT-β and is shown to be advantageous when processing signals corrupted by both independent noise and reverberation effects. Simulations show superior performance for the time-domain implementation under conditions of independent noise for time-limited broadband signals, achieving low estimation errors at signal-to-noise ratios 8 to 13 dB lower than that required for a frequency-domain implementation. Extensive Monte Carlo simulations are also performed for the time-domain delay estimator using the PHAT-β on speech signals corrupted by reverberation and independent noise. Performance metrics include percent anomalous detections as well as the root mean square estimation error. Results show that partial whitening leads to significant improvements over zero or total whitening (as in the case of the standard PHAT). Simulations indicate that robust performance can be achieved for β values near 0.4 when both reverberations and independent noises are present.