The advent of high throughput data has led to a massive increase in the number of hypothesis tests conducted in many types of biological studies and a concomitant increase in stringency of significance thresholds. Filtering methods, which use independent information to eliminate less promising tests and thus reduce multiple testing, have been widely and successfully applied. However, key questions remain about how to best apply them: When is filtering beneficial and when is it detrimental? How good does the independent information need to be in order for filtering to be effective? How should one choose the filter cutoff that separates tests that pass the filter from those that dont?