Abstract In digital pathology, image segmentation algorithms are usually ranked on clean, benchmark datasets. However, annotations in digital pathology are hard, time-consuming and by nature imperfect. We expand on the SNOW (Semi-, Noisy and/or Weak) supervision concept introduced in an earlier work to characterize such data supervision imperfections. We analyse the effects of SNOW supervision on typical DCNNs, and explore learning strategies to counteract those effects. We apply those lessons to the real-world task of artefact detection in whole-slide imaging. Our results show that SNOW supervision has an important impact on the performances of DCNNs and that relying on benchmarks and challenge datasets may not always be relevant for assessing algorithm performance. We show that a learning strategy adapted to SNOW supervision, such as “Generative Annotations", can greatly improve the results of DCNNs on real-world datasets.