The relaxed zero-forcing (RZF) beamformer is a quadratically-and-linearly constrained minimum variance beamformer. The central question addressed in this paper is whether RZF performs better than the widely-used minimum variance distortionless response and zero-forcing beamformers under temporally-correlated interference. First, RZF is rederived by imposing an ellipsoidal constraint that bounds the amount of interference leakage for mitigating the intrinsic gap between the output variance and the mean squared error (MSE) which stems from the temporal correlations. Second, an analysis of RZF is presented for the single-interference case, showing how the MSE is affected by the spatio-temporal correlations between the desired and interfering sources as well as by the signal and noise powers. Third, numerical studies are presented for the multiple-interference case, showing the remarkable advantages of RZF in its basic performance as well as in its application to brain activity reconstruction from EEG data. The analytical and experimental results clarify that the RZF beamformer gives near-optimal performance in some situations.