In epigenome-wide association studies, cell-type composition often differs between cases and controls, yielding associations that simply tag cell type rather than reveal fundamental biology. Current solutions require actual or estimated cell-type composition--information not easily obtainable for many samples of interest. We propose a method, FaST-LMM-EWASher, that automatically corrects for cell-type composition without the need for explicit knowledge of it, and then validate our method by comparison with the state-of-the-art approach. Corresponding software is available from http://www.microsoft.com/science/.