We present a new technique for adaptive band selection from hyperspectral image cubes for detecting small targets using an anomaly detector. The proposed technique ensures the selection of lowest number of spectral bands using Mahalanobis distance, maximum affordable extra noise variance, and Constant False Alarm Rate (CFAR) anomaly detector threshold. Since the target is small, band selection based only on Mahalanobis distance is not adequate and the bands which can withstand extra noise should be chosen. In addition, thresholding must be considered to avoid misclassification of target. The proposed technique yields comparatively low false alarm rate even with a few bands. For real time applications, acousto-optic tunable filter based spectral imagers may be used for acquiring hyperspectral images and for selecting the bands.