This paper describes theory, computational algorithms, and software associated with the DISCRETE edit system. The prototype DISCRETE edit system is based on the Fellegi-Holt model (JASA 1976) of editing. A new implicit-edit generation algorithm replaces an algorithm of Garfinkel, Kunnathur, and Liepins (Operations Research 1986). A characterization specific to the edit situation reduces the amount of information needed in the integer programs used for error localization. Even with moderate-size problems, computation during error localization is reduced by two orders of magnitude.