The usefulness of two-class statistical classifiers is limited when one or both of the conditional misclassification rates is unacceptably high. Incorporating a neutral zone region into the classifier provides a mechanism to refer ambiguous cases to follow-up where additional information might be obtained to clarify the classification decision. Through the use of the neutral zone region, the conditional misclassification rates can be controlled and the classifier becomes useful. Three real-life examples, including applications to prostate cancer and kidney dysfunction following heart surgery, are used to illustrate how neutral zone regions can extract utility from disappointing classifiers that might otherwise be abandoned.