Typical speech enhancement algorithms operate on the shorttime magnitude spectrum, while keeping the short-time phase spectrum unchanged for synthesis. Recently, a novel approach to speech enhancement has been proposed where the noisy magnitude spectrum is recombined with a changed phase spectrum to produce a modified complex spectrum. During synthesis the low energy components of the modified complex spectrum cancel out more than the high energy components, thus reducing background noise. In the present work, a procedure that employs noise estimates to compensate the phase spectrum for additive noise distortion is formulated. The proposed approach is objectively evaluated against several popular speech enhancement methods under various noise conditions and is shown to compare favourably