High-dimensional association testing in biomedical sciences can be improved by using informative covariates. A new method for controlling type-1 error rates in this setting has been developed, which significantly boosts power compared to existing methods. By mapping observations independently, the method enhances the accuracy of conditional false discovery rate estimation. This approach was tested on transcriptome-wide association studies and can be iteratively applied with multiple covariates, leading to substantial improvements in analysis power and applicability.