Anomaly detection attempts to identify instances in the data that do not conform to the expected behavior. Because it is often difficult to label instances, the problem is tackled in an unsupervised way by employing data-driven heuristics to identify anomalies. However, the heuristics are imperfect which can degrade a detector’s performance. One way to mitigate this problem is using Active Learning to collect labels that help correct cases where the employed heuristics are incorrect. Alternatively, one can allow the detector to abstain (i.e., say “I do not know”) whenever it is likely to make mispredictions at test time, which is called Learning to Reject (LtR). However, while both have been studied in the context of anomaly detection, they have not been considered in conjunction. Although they both need labels to accomplish their task, integrating these two ideas is challenging for two reasons. First, their label selection strategies are intertwined but they acquire different types of labels. Second, it is unclear how to best divide the limited budget between labeling instances that help AL and those that help LtR. In this paper, we introduce SADAL, the first semi-supervised detector that allocates the label budget between AL and LtR by relying on a reward-based selection function. Experimentally on 25 datasets, we show that our approach outperforms several baselines by achieving a better performance.