Incremental truncation is a method for constructing libraries of every one base pair truncation of a segment of DNA. Incremental truncation libraries can be created using a time-dependent nuclease method or through the incorporation of alpha-phosphothioate dNTPs by PCR or by primer extension (THIO(pcr) truncation and THIO(extension) truncation, respectively). Libraries created by the fusion of two truncation libraries, known as ITCHY libraries, can be created using the above methods or by the incremental truncation-like method SHIPREC. Knowing and being able to tailor the distribution of truncations in incremental truncation, ITCHY and SHIPREC libraries would be beneficial for their use in protein engineering and other applications. However, the experimental determination of the distributions would require extensive, cost-prohibitive, DNA sequencing to obtain statistically relevant data. Instead, a theoretical prediction of the distributions was developed. Time-dependent incremental truncation libraries had the most uniform distribution of truncation lengths, but were biased against longer truncations. Essentially uniform distribution over the desired truncation range (from zero to N-max base pairs) required that truncations be prepared up to at least 1.2-1.5 N-max. THIC(pcr) and THIO(extension) truncation libraries had a very nonuniform distribution of truncation lengths with a bias against longer truncations. Such nonuniformity could be significantly diminished by decreasing the incorporation rate of alphaS-dNTPs but at the expense of having a large fraction of the DNA truncated beyond the desired range or completely degraded. ITCHY libraries created using time-dependent truncation had the most uniform distribution of possible fusions and had the highest fraction of the library being parental-length fusions. However, the distribution of parental-length fusions was biased against fusions near the beginning/ends of genes unless the truncation libraries are prepared with a uniform distribution up to N-max. In contrast, SHIPREC libraries and THIO(pcr) ITCHY libraries, by the very nature of the nonuniform distributions of the truncated DNA, are ensured of having a uniform distribution of fusion points in parental-length fusions. This comes at the expense of having a smaller fraction of the library being parental-length fusions; however, this limitation can be overcome by performing size selection on the library. (C) 2003 Wiley Periodicals, Inc.