Given the size of digitized Whole Slide Images (WSIs), it is generally laborious and time-consuming for pathologists to exhaustively delineate objects within them, especially with datasets containing hundreds of slides to annotate. Most of the time, only slide-level labels are available, giving rise to the development of weakly-supervised models. However, it is often difficult to obtain from such models accurate object localization, e.g., patches with tumor cells in a tumor detection task, as they are mainly designed for slide-level classification. Using the attention-based deep Multiple Instance Learning (MIL) model as our base weakly-supervised model, we propose to use mixed supervision-i.e., the use of both slide-level and patch-level labels-to improve both the classification and the localization performances of the original model, using only a limited amount of patch-level labeled slides. In addition, we propose an attention loss term to regularize the attention between key instances, and a paired batch method to create balanced batches for the model. First, we show that the changes made to the model already improve its performance and interpretability in the weakly-supervised setting. Furthermore, when using only between 12 and 62% of the total available patch-level annotations, we can reach performance close to fully-supervised models on the tumor classification datasets DigestPath2019 and Camelyon16.