This chapter discusses the unidirectional digestion with exonuclease III in deoxyribonucleic acid (DNA) sequence analysis. The chapter describes a rapid strategy and a simplified version related to the uniform rate at which Escherichia coli exonuclease III can digest DNA from one end. This strategy can be used with single-stranded phage, plasmid, and synthetic RNA-plasmid systems. The reagents that are used are inexpensive and readily available. The chapter illustrates a figure that outlines the steps involved in generating the ordered sets of deletion breakpoints for DNA sequencing. The method is based on a series of enzymatic treatments of a segment of DNA cloned into a suitable vector. Cloning efficiencies are sufficiently high that standard Ca2+ treated cells are adequate for transfection or transformation. Exonuclease III is an incompletely processive nuclease. The rate of exonuclease III is very sensitive to the temperature of incubation. The procedure described in the chapter has several advantages. Most importantly, it yields cloned breakpoints at high efficiency that are tightly clustered around a particular point in the sequence, greatly reducing the tedious screening steps required to fill in gaps in the sequence.