A DNA structure is described that can cleave single-stranded DNA oligonucleotides in the presence of ionic copper. This "deoxyribozyme" can self-cleave or can operate as a bimolecular complex that simultaneously makes use of duplex and triplex interactions to bind and cleave separate DNA substrates. Bimolecular deoxyribozyme-mediated strand scission proceeds with a kobs of 0.2 min-1, whereas the corresponding uncatalyzed reaction could not be detected. The duplex and triplex recognition domains can be altered, making possible the targeted cleavage of single-stranded DNAs with different nucleotide sequences. Several small synthetic DNAs were made to function as simple "restriction enzymes" for the site-specific cleavage of single-stranded DNA.