Abstract: We study the problem of classification with a reject option for a fixed predictor, crucial to natural language processing. We introduce a new problem formulation for this scenario, and an algorithm minimizing a new surrogate loss function. We provide a complete theoretical analysis of the surrogate loss function with a strong $H$-consistency guarantee. For evaluation, we choose the \textit{decontextualization} task, and provide a manually-labelled dataset of $2\mathord,000$ examples. Our algorithm significantly outperforms the baselines considered, with a $\sim 25$% improvement in coverage when halving the error rate, which is only $\sim 3$% away from the theoretical limit.