This paper investigates if and how oversampling techniques can be applied in a useful manner to hyperspectral images. Oversampling occurs when the signal is sampled higher than the Nyquist frequency. If this occurs, the higher sampling rate can be traded for precision. Specifically, one bit of precision can be gained if the signal has been oversampled by a factor of four. This paper first investigates if spectral oversampling actually occurs in hyperspectral images, then looks at its usefulness in classification. Simulations were done with synthetic and real images. The results indicate that oversampling does occur for many real objects, so a knowledge of what is being searched for is crucial for knowing if oversampling techniques can be used. The classification results indicate that it takes a relatively large amount of noise for these techniques to have a significant impact on classification with synthetic images. For real images however, an improvement in classification for both supervised and unsupervised algorithms was observed for all simulations.