In radar applications, adaptive beampatterns with low sidelobes and stable mainlobe shapes are desired to suppress pulsed deceptive jammers or sidelobe targets and to accurately measure the direction-of-arrival (DOA) of a target using monopulse techniques. In practice, all kinds of errors exist, such as signal pointing errors, array calibration errors and array covariance matrix estimation errors. In the presence of these errors, adaptive beamformers can suffer from severe performance degradations, including poor interference rejection, distorted mainlobes, and high sidelobes. In this paper, we investigate how a quadratic constraint based adaptive beamformer with peak sidelobe control, referred to as the PPSC (precise peak sidelobe control) method, can be combined with a signal removal scheme to achieve desired adaptive beampatterns and interference rejection performance for a uniform linear array. Numerical results are provided to demonstrate the performance of the proposed method.