This paper presents a generic beamformer design algorithm for arbitrary microphone array geometry. It makes efficient use of noise models for ambient and instrumental and microphone directivity patterns. By using a new definition of the target criterion and replacing a multi-dimensional optimization with a much simpler one-dimensional search, we can compute near-optimal solutions in reasonable time. The designed beams achieve noise suppression levels between 10 and 15 dB, for microphone arrays with four to eight elements, and linear and circular geometries. The fast beamformer real-time processing engine consumes less than 2% of the CPU power of a modern personal computer, for a four-microphone array.