Recent self-supervised models have demonstrated equal or better performance than supervised methods, opening for AI systems to learn visual representations from practically unlimited data. However, these methods are typically classification-based and thus ineffective for learning high-resolution feature maps that preserve precise spatial information. This work introduces superpixels to improve self-supervised learning of dense semantically rich visual concept embeddings. Decomposing images into a small set of visually coherent regions reduces the computational complexity by $\mathcal{O}(1000)$ while preserving detail. We experimentally show that contrasting over regions improves the effectiveness of contrastive learning methods, extends their applicability to high-resolution images, improves overclustering performance, superpixels are better than grids, and regional masking improves performance. The expressiveness of our dense embeddings is demonstrated by improving the SOTA unsupervised semantic segmentation benchmark on Cityscapes, and for convolutional models on COCO.