A relevance filter is proposed which removes features based on the mutual information between class labels and features. It is proven that both feature independence and class conditional feature independence are required for the filter to be statistically optimal. This could be shown by establishing a relationship with the conditional relative entropy framework for feature selection. Removing features at various significance levels as a preprocessing step to sequential forward search leads to a huge increase in speed, without a decrease in classification accuracy. These results are shown based on experiments with 5 high-dimensional publicly available gene expression data sets.