Single base-pair overhangs are poor substrates for T4 DNA ligase: they anneal very poorly, and are as difficult to ligate as are blunt ended DNA fragments. Also, for AlwI the overhang is not constrained to be any particular nucleotide; all four bases are roughly equally represented. Consequently, any given overhang is compatible with only 25% of the other overhangs present. This lowers ligation efficieny relative to overhangs generated by restriction enzymes which leave only mutually compatible overhangs.  Ligation efficiency can be increased by using our Blunt/TA Ligase Master Mix.