One of the challenges with the implementation of multi-microphone noise reduction systems in practical applications lies in the need for the knowledge of the speech and noise covariance matrices. Recently, a method based on Maximum Likelihood (ML) estimation addressed this problem. Despite its relative success in practical setups, this method may suggest negative spectral components for the clean speech due to noise influences. In this paper, we suggest a new estimation technique that tackles this issue by enforcing a power constraint on the estimation problem. We compare the proposed method with the ML method both in synthetic and real-life scenarios using objective measures. The results suggest that the proposed method can improve speech quality without a loss of intelligibility.