For audio source separation applications, it is common to apply a Wiener-like filtering to a time-frequency (TF) representation of the data, such as the short-time Fourier transform (STFT). This approach , in which the phase of the original mixture is assigned to each component, is limited when sources overlap in the TF domain. In this paper, we propose to improve this technique by accounting for two properties of the phase. First, we model the sources by anisotropic Gaussian variables: this model accounts for the non-uniformity of the phase, and permits us to incorporate some prior information about the phase that originates from a sinusoidal model. Second, we exploit the STFT consistency, which is the relationship between STFT coefficients that is due to the redundancy of the STFT. We derive a conjugate gradient algorithm for estimating the corresponding filter, which we refer to as the consistent anisotropic Wiener filter. Experiments conducted on music pieces show that the proposed approach yields results similar to or better than the state-of-the-art with a dramatic reduction of the computation time.