Coherent fading noise (also known as speckle noise) affects the SNR and sensitivity of Distributed Acoustic Sensing (DAS) systems and makes them random processes of position and time. As in speckle noise, the statistical distribution of DAS SNR is particularly wide and its standard deviation (STD) roughly equals its mean (σSNRSNR 0.89). Trading resolution for SNR may improve the mean SNR but not necessarily narrow its distribution. Here a new approach to achieve both SNR improvement (by sacrificing resolution) and narrowing of the distribution is introduced. The method is based on acquiring high resolution complex backscatter profiles of the sensing fiber, using them to compute complex power profiles of the fiber which retain phase variation information and filtering of the power profiles. The approach is tested via a computer simulation and demonstrates distribution narrowing up to σSNRSNR < 0.2.