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Under conditions of low sample support, a low-rank solution of the minimum variance distortionless response (MVDR) equations can yield a higher output signal-to-interference-plus-noise ratio (SINR) than the full-rank MVDR beamformer. In this paper, we investigate several low-rank beam- forming techniques, and we also propose a new beamformer that we refer to as the indirect dominant mode rejection (IDMR). We analyze the degradation in the output SINR caused by residual cross correlations embedded in the sampled covariance matrix due to low sample support. The IDMR beamformer is based on a parametric estimate of the covariance matrix, in which any cross correlation is canceled out. Simulations reveal that the IDMR beamformer yields a dramatic improvement in output SINR relative to the conjugate gradient (CG), principal component inverse (PCI), and dominant mode rejection (DMR) beamformers. In our investigation of the low-rank CG beamformer, we address the issue of whether the unity gain constraint in the look direction should be enforced a priori via the use of a blocking matrix or effected a posteriori through simple scaling of the beamforming vector. Remarkably, it is proven that the two methods yield exactly the same low-rank beamformer at each and every rank.