The presence of irrelevant and correlated data points in a Raman spectrum can lead to a decline in classifier performance. We introduce support vector machine (SVM)-based recursive feature elimination into the field of Raman spectroscopy and demonstrate its performance on a data set of spectra of clinically relevant microorganisms in urine samples, along with patient samples. As the original technique is only suitable for two-class problems, we adapt it to the multi-class setting. It is shown that a large amount of spectral points can be removed without degrading the prediction accuracy of the resulting model notably.