Virtually all of deep learning literature relies on the assumption of large amounts of available training data. Indeed, even the majority of few-shot learning methods rely on a large set of base classes for pretraining. This assumption, however, does not always hold. For some tasks, annotating a large number of classes can be infeasible, and even collecting the images themselves can be a challenge in some scenarios. In this paper, we study this problem and call it Small Data setting, in contrast to Big Data. To unlock the full potential of small data, we propose to augment the models with annotations for other related tasks, thus increasing their generalization abilities. In particular, we use the richly annotated scene parsing dataset ADE20K to construct our realistic Long-tail Recognition with Diverse Supervision (LRDS) benchmark by splitting the object categories into head and tail based on their distribution. Following the standard few-shot learning protocol, we use the head classes for representation learning and the tail classes for evaluation. Moreover, we further subsample the head categories and images to generate two novel settings which we call Scarce-Class and Scarce-Image, respectively corresponding to the shortage of samples for rare classes and training images. Finally, we analyze the effect of applying various additional supervision sources under the proposed settings. Our experiments demonstrate that densely labeling a small set of images can indeed largely remedy the small data constraints.