An expression in closed form is derived for the recognition error vs. rejection rate of optical character or word recognition systems. This expression allows to define a lower bound for the error rate of any recognition system employing a rejection process based on the definition of a confidence threshold. This relation has also proved to be useful to make a quantitative comparison between two confidence computation methods implemented in a system for reading USA Census '90 hand-written forms. The newly proposed method is based upon a confidence model integrating single-character confidence levels, digram statistics and other information from the dictionary matching phase. At a 50% rejection rate, the field error rate calculated using the new confidence computation algorithm decreased from 47.7% to 44.6%, which represents a considerable improvement, given a theoretical lower bound of 40.8% on the error rate.