Multi-task learning is central to many real-world applications. Unfortunately, obtaining labelled data for all tasks is time-consuming, challenging, and expensive. Active Learning (AL) can be used to reduce this burden. Existing techniques typically involve picking images to be annotated and providing annotations for all tasks. In this paper, we show that it is more effective to select not only the images to be annotated but also a subset of tasks for which to provide annotations at each AL iteration. Furthermore, the annotations that are provided can be used to guess pseudo-labels for the tasks that remain unannotated. We demonstrate the effectiveness of our approach on several popular multi-task datasets.