Exonuclease III (Exo III) will digest double-stranded DNA in a 3′ to 5′ direction if the DNA is blunt-ended or possesses a 5′ overhang. It will not digest if there is a 3′ overhang of three or more bases, or if the 3’ end has had thiophosphate-containing bases incorporated into it. In order to generate a set of insert deletions using Exo III it is necessary to cut the polylinker twice with different restriction enzymes so that the cut end nearest the primer site possesses a 3′ overhang, or has thiophosphate residues at the 3′ end, and the end of the polylinker attached to the insert possesses a 5′ overhang or blunt end. If this can be achieved, digestion with Exo III will result in progressive deletion of the 3′ end of the insert, leaving a single-stranded 5′ overhang that can be removed by treatment with mung bean nuclease (1) or exonuclease VII (Exo VII). The blunt ends thus formed are ligated, a suitable host transformed, and colonies are picked at random and screened for insert size (2), following which a suitable range of inserts is then sequenced.