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Annotating datasets for question answering (QA) tasks is very costly, as it requires intensive manual labor and often domain-specific knowledge. Yet strategies for annotating QA datasets in a cost-effective manner are scarce. To provide a remedy for practitioners, our objective is to develop heuristic rules for annotating a subset of questions, so that the annotation cost is reduced while maintaining both in- and out-of-domain performance. For this, we conduct a large-scale analysis in order to derive practical recommendations. First, we demonstrate experimentally that more training samples contribute often only to a higher in-domain test-set performance, but do not help the model in generalizing to unseen datasets. Second, we develop a model-guided annotation strategy: it makes a recommendation with regard to which subset of samples should be annotated. Its effectiveness is demonstrated in a case study based on domain customization of QA to a clinical setting. Here, remarkably, annotating a stratified subset with only 1.2% of the original training set achieves 97.7% of the performance as if the complete dataset was annotated. Hence, the labeling effort can be reduced immensely. Altogether, our work fulfills a demand in practice when labeling budgets are limited and where thus recommendations are needed for annotating QA datasets more cost-effectively.