In this paper, we present a new adaptive microphone array processing algorithm for hands-free sound capture. Most traditional adaptive beamforming techniques operate solely on the basis of the direction of arrival of the desired source and are blind to any knowledge about the signal itself. In contrast, the proposed algorithm uses a nonlinear spatial filter to generate an estimate of the magnitude of the source signal. This estimate is then used to drive the adaptation of a linear beamformer according to a log-MMSE criterion. By combining a nonlinear spatial filter with an adaptive beamformer in this manner, we are able to exploit the high SNR output from the nonlinear spatial filter to drive a linear beamformer that does not suffer from distortions or artifacts. A series of experiments demonstrate that the proposed method generates improvements in PESQ and SNR over conventional methods.