Methods of preparing double-stranded nucleic acids with single-stranded overhangs for amplification and sequencing are disclosed. Contacting a blunt-ended double-stranded nucleic acid molecules with Taq results in non-templated directed addition of a single nucleotide to the 3′ ends of the nucleic acid with A added most frequently followed by G followed by C and T. G tailing is sufficiently frequent that the efficiency of ligation of nucleic acid molecules to adapters can be significantly increased by including adapters tailed with T and C. The ligation efficiency can be increased even further with blunted-ended adapters to ligate to blunt-ended nucleic acid molecules that failed to undergo tailing.