While large-scale studies applying various statistical approaches have identified hundreds of mutated driver genes across various cancer types, the contribution of epigenetic changes to cancer remains more enigmatic. This is partly due to the fact that certain regions of the cancer genome, due to their genomic and epigenomic properties, are more prone to dysregulated DNA methylation than others. Thus, it has been difficult to distinguish which promoter methylation changes are really driving carcinogenesis from those that are mostly just a reflection of their genomic location. By developing a novel method that corrects for epigenetic covariates, we reveal a small, concise set of potential epigenetic driver events. Interestingly, those changes suggest different modes of epigenetic carcinogenesis: first, we observe recurrent inactivation of known cancer genes across tumour types suggesting a higher convergence on common tumour suppressor pathways than previously anticipated. Second, in prostate cancer, a cancer type with few recurrently mutated genes, we demonstrate how the epigenome primes tumours towards higher tolerance of other aberrations.