Evidence suggests that networks trained on large-scale datasets such as ImageNet generalize well not solely because of the numerous training examples, but also the class diversity which encourages learning of enriched features. This raises the question of whether this remains true when data is scarce - is there an advantage to learning with additional labels in low-data regimes? In this work, we consider a task that requires difficult-to-obtain expert annotations: tumor segmentation in mammography images. We show that, in low-data settings, performance can be improved by complementing the expert annotations with seemingly uninformative labels from non-expert annotators, turning the task into a multi-class problem. We reveal that these gains increase when less expert data is available, and uncover several interesting properties through further studies. We demonstrate our findings on a new dataset that we introduce here, ANON, and confirm them on two public datasets.