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For safety-critical applications such as autonomous driving, CNNs have to be robust with respect to unavoidable image corruptions, such as image noise. While previous works addressed the task of robust prediction in the context of full-image classification, we consider it for dense semantic segmentation. We build upon an insight from image classification that output robustness can be improved by increasing the network-bias towards object shapes. We present a new training schema that increases this shape bias. Our basic idea is to alpha-blend a portion of the RGB training images with faked images, where each class-label is given a fixed, randomly chosen color that is not likely to appear in real imagery. This forces the network to rely more strongly on shape cues. We call this data augmentation technique ``Painting-by-Numbers''. We demonstrate the effectiveness of our training schema for DeepLabv3+ with various network backbones, MobileNet-V2, ResNets, and Xception, and evaluate it on the Cityscapes dataset. With respect to our 16 different types of image corruptions and 5 different network backbones, we are in 74% better than training with clean data. For cases where we are worse than a model trained without our training schema, it is mostly only marginally worse. However, for some image corruptions such as images with noise, we see a considerable performance gain of up to 25%.