Generating training sets for deep convolutional neural networks is a bottleneck for modern real-world applications. This is a demanding tasks for applications where annotating training data is costly, such as in semantic segmentation. In the literature, there is still a gap between the performance achieved by a network trained on full and on weak annotations. In this paper, we establish a strategy to measure this gap and to identify the ingredients necessary to close it. On scribbles, we establish state-of-the-art results comparable to the latest published ones Tang et al. 2018: we obtain a gap in mIoU of 2.4% without CRF (2.8% in Tang et al., 2018, arXiv:1804.01346), and 2.9% with CRF post-processing (2.3% in Tang et al. 2018). However, we use completely different ideas: combining local and global annotator models and regularising their prediction to train DeepLabV2. Finally, closing the gap was reported only recently for bounding boxes in Khoreva et al., by requiring 10x more training images. By simulating varying amounts of pixel-level annotations respecting scribble human annotations statistics, we show that our training strategy reacts to small increases in the amount of annotations and requires only 2-5x more annotated pixels, closing the gap with only 3.1% of all pixels annotated. This work contributes new ideas towards closing the gap in real-world applications.