We propose a simple two-pass beamforming scheme that combines adaptive and nonadaptive methods to achieve high-quality ultrasound images at low computational cost. During the first pass, our beamformer processes buffered input vectors using an inexpensive nonadaptive method and computes the corresponding envelope. Based on that envelope information, selected outputs may be recomputed during the second pass (to improve beamforming performance) using an expensive adaptive method. The purpose of the first pass is to identify which nonadaptively-beamformed outputs can be spared from a heavy computational load of adaptive beamforming taking place during the second pass. In t his work, our beamforming scheme combines the nonadaptive delay-and-sum (DAS) beamformer and the adaptive Generalized Sidelobe Canceller (GSC), and it selects outputs for recomputation based on a threshold window. We have evaluated our scheme using simulated ultrasound images of a 12-point phantom and a point-scatterer-cyst phantom, achieving substantial threshold-dependent computational savings while maintaining acceptable image resolution and contrast, compared to pure GSC beamforming.