Semantic labelling and instance segmentation are two tasks that require particularly costly annotations. Starting from weak supervision in the form of bounding box detection annotations, we propose a new approach that does not require modification of the segmentation training procedure. We show that when carefully designing the input labels from given bounding boxes, even a single round of training is enough to improve over previously reported weakly supervised results. Overall, our weak supervision approach reaches ~95% of the quality of the fully supervised model, both for semantic labelling and instance segmentation.