A standard classifier is forced to predict the label of every test instance, even when confidence in the predictions is very low. In many scenarios, it would, however, be better to avoid making these predictions, maybe leaving them to a human expert. A classifier with that alternative is referred to as a classifier with reject option. In this paper, we propose an algorithm that, for a particular data set, automatically suggests a number of accuracy levels, which it will be able to meet perfectly, using a classifier with reject option. Since the basis of the suggested algorithm is conformal prediction, it comes with strong validity guarantees. The experimentation, using 25 publicly available two-class data sets, confirms that the algorithm obtains empirical accuracies very close to the requested levels. In addition, in an outright comparison with probabilistic predictors, including models calibrated with Platt scaling, the suggested algorithm clearly outperforms the alternatives.