Zinc fingers are small DNA-binding modules noted for their occurrence in a large number of eukaryotic transcription factors, and their use in protein engineering. Although it was expected that zinc fingers can bind to a wide diversity of DNA sequences, previous studies using model zinc finger domains from Zif268 (and Sp1) have revealed a potential limitation to the DNA-binding specificity. For example, phage display selection of individual zinc fingers to recognize trinucleotide DNA subsites returned fingers that bound specifically only to triplets of the form GNN, i.e., triplets with guanine at the 5' end. Following our recently reported work [Isalan, M., Choo, Y., and Klug, A. (1997) Proc. Natl. Acad. Sci. U.S.A. 94, 5617-5621], we now show that this limitation can be overcome by the concerted randomization of certain amino acid positions in adjacent zinc fingers that specify overlapping DNA subsites. This illustrates an important mechanism underlying DNA recognition by arrays of zinc fingers, and points the way to improved strategies for the design of highly specific zinc finger proteins that bind any given nucleotide sequence.