A key feature when designing DNA targeting tools and especially nucleases is specificity. The ability to control and tune this important parameter represents an invaluable advance to the development of such molecular scissors. Here, we identified and characterized new non-conventional RVDs (ncRVDs) that possess novel intrinsic targeting specificity features. We further report a strategy to control TALEN targeting based on the exclusion capacities of ncRVDs (discrimination between different nucleotides). By implementing such ncRVDs, we demonstrated in living cells the possibility to efficiently promote TALEN-mediated processing of a target in the HBB locus and alleviate undesired off-site cleavage. We anticipate that this method can greatly benefit to designer nucleases, especially for therapeutic applications and synthetic biology.