Modified nucleic acid adapters are provided that collectively provide a mixture of nucleotides at the 3′ end of 5′ adapters and at the 5′ end of 3′ adapters such that at least one adapter in each set has any given nucleotide at position 1, i.e., the nucleotide position available for ligation to a small RNA, and has any given nucleotide at position 2 adjacent to position 1 for use in overcoming bias during nucleic acid manipulation, such as small RNA characterization and/or profiling by, e.g., deep sequencing, along with methods for use of the modified adapters in small RNA characterization. The modified adapters have at least two mixed nucleotides at the adapter terminus to be ligated to a nucleic acid such as a small RNA.