In real-world data labeling, annotators often provide imperfect labels. It is thus common to employ multiple annotators to label data with some overlap between their examples. We study active learning in such settings, aiming to train an accurate classifier by collecting the fewest total annotations. Here we propose ActiveLab, a practical method to decide what to label next that works with any classifier model and can be used in pool-based batch active learning with one or multiple annotators. ActiveLab automatically estimates when it is more informative to re-label examples vs. labeling entirely new ones. This is a key aspect of producing high quality labels and trained models within a limited annotation budget. In experiments on image and tabular data, ActiveLab reliably trains more accurate classifiers with far fewer annotations than a wide variety of popular active learning methods.