The auxiliary vector (AV) algorithm iteratively generates a sequence of filters that converge to the minimum variance distortionless response filter. The early, nonasymptotic elements generated by this algorithm offer favorable bias/variance characteristics and outperform in mean-square filter estimation error, filters generated by other iterative methods. This paper develops two new algorithms for selecting the best AV filter: a MMSE method that can either utilize a training sequence or can operate in a blind decision-directed mode, and a cyclostationary method that exploits the property that cyclostationary signals generate spectral lines when certain nonlinear transformations are applied to them. These new methods are simulated along with previously derived methods in an adaptive beamforming application, and compared with other common beamforming algorithms.