Controlling the resolution in adaptive beamformers is often crucial. A simple method that works for both narrowband and broad-band arrays is presented. This method is based on the normalized leaky LMS algorithm in conjunction with a generalized sidelobe canceller (GSC) structure, where the GSC is designed using a spatial filtering approach. In essence, the suppression of the spatial filters and the implicit noise of the leaky LMS algorithm together determine the adaptive beamformer. Analytical expressions are given for the Wiener filters and the output spectrum versus frequency and point source location. These expressions are employed in the design specification of the spatial filters and to obtain conditions for a controlled quiescent beamformer response. Simulation results are presented to illustrate the behavior of the array.