For some time, compact acoustic vector sensors (AVSs) capable of sensing particle velocity in three orthogonal directions have been used in underwater acoustic sensing applications. Potential advantages of using AVSs in air include substantial noise reduction with a very small aperture and few channels. For this study, a four-microphone array approximating a small (1cm3) AVS in air was constructed using three gradient microphones and one omnidirectional microphone. This study evaluates the signal extraction performance of one nonadaptive and four adaptive beamforming algorithms. Test signals, consisting of two to five speech sources, were processed with each algorithm, and the signal extraction performance was quantified by calculating the signal-to-noise ratio (SNR) of the output. For a three-microphone array, robust and nonrobust versions of a frequency-domain minimum-variance (FMV) distortionless-response beamformer produced SNR improvements of 11to14dB, and a generalized sidelobe canceller (GSC) produced improvements of 5.5to8.5dB. In comparison, a two-microphone omnidirectional array with a spacing of 15cm yielded slightly lower SNR improvements for similar multi-interferer speech signals.