Fluctuations are always present in underwater sound propagation, and are generally viewed as a complication in signal detection and identification. However, in some cases where the signals fluctuate less than the noise, it is possible to take advantage of the different magnitudes of fluctuations of signal and noise to improve detection. Wagstaff's integration silencing processor (WISPR) is an example of such a processor. The original version of the WISPR processor utilized power values derived from complex pressures in a given frequency bin, but ignored the phases of these complex pressures. An improved processor that takes advantage of the phase as well as the amplitude is described below. Its performance is verified using measured data, where detection has been accomplished by a margin of 4 decibels. Simulations using synthetic data show that the new processor can be effective for signal-to-noise ratios greater than minus 20 decibels.