In the paper, a simple beam-forming approach is used to estimate the direction of arrival of plane waves in white noise. The basic idea of the approach is to minimise the mean-square value of the difference between the actual array response and the desired unity response in certain directional regions while imposing directional eigenvector constraints obtained from the correlation matrix. This is illustrated with numerical results. The connection between this bearing estimation scheme and the minimum norm spatial spectral estimator is also discussed.