Contemporary high-resolution Direction-Of-Arrival (DOA) techniques in sensor array processing based on the MUSIC algorithm fail when the signals are fully correlated and/or closely spaced. When the data are taken from a linear array of equally-spaced sensors, spatial smoothing or subarray averaging is the most familiar way to combat the effects of signal correlation and retain some computational efficiency. The purpose of this paper is to show analytically that improved parameter estimates result when subarray averaging is applied to a suitable reduced-rank approximation to the array covariance matrix instead of performing a conventional spatial smoothing. Further improvements can be achieved if a suitable data matrix is utilized. Simulation examples are provided to substantiate the theoretical predictions.