DS adapters are constructed by annealing two oligonucleotides, one of which contains a 12-nt singlestranded randomized tag sequence. A DNA polymerase is used to copy the degenerate tag sequence, thereby converting it to a double-stranded form (Fig. 3). The extended product contains an HpyCH4III restriction site downstream of the tag sequence. Cleavage of this site results in a 3′ dT overhang on the end of the final adapter (Figs. 1a and 3b), which can be ligated to the 3′ dA overhang on the DNA fragment library to be sequenced. Twelve random nucleotides per adapter (24 nt per final ligated molecule) significantly exceed the degeneracy needed to ensure unique labeling of every molecule in a library. However, a tag length of <12 is incompatible with the Illumina sequencer because of technical limitations of the platform’s ‘phasing’ requirement and should be avoided.