Binary classifier systems that provide class membership probabilities as outputs may be augmented by a reject option to refuse classification for cases that either appear to be outliers, or for which the output probability is around 0.5. We investigated the effect of these two reject options (called "distance reject" and "ambiguity reject", respectively) on the calibration and discriminatory power of logistic regression models. Outliers were found using one-class support vector machines. Discriminatory power was measured by the area under the ROC curve, and calibration by the Hosmer-Lemeshow goodness-of-fit test. Using an artificial data set and a real-world data set for diagnosing myocardial infarction, we found that ambiguity reject increased discriminatory power, while distance reject decreased it. We did not observe any influence of either reject option on the calibration of the logistic regression models.