Transcription activator-like effectors (TALEs) are important Xanthomonas virulence factors that bind DNA via a unique tandem 34-amino-acid repeat domain to induce expression of plant genes. So far, TALE repeats are described to bind as a consecutive array to a consecutive DNA sequence, in which each repeat independently recognizes a single DNA base. This modular protein architecture enables the design of any desired DNA-binding specificity for biotechnology applications. Here we report that natural TALE repeats of unusual amino-acid sequence length break the strict one repeat-to-one base pair binding mode and introduce a local flexibility to TALE–DNA binding. This flexibility allows TALEs and TALE nucleases to recognize target sequence variants with single nucleotide deletions. The flexibility also allows TALEs to activate transcription at allelic promoters that otherwise confer resistance to the host plant.