We introduce NeCo: Patch Neighbor Consistency, a novel self-supervised training loss that enforces patch-level nearest neighbor consistency across a student and teacher model. Compared to contrastive approaches that only yield binary learning signals, i.e. "attract" and "repel", this approach benefits from the more fine-grained learning signal of sorting spatially dense features relative to reference patches. Our method leverages differentiable sorting applied on top of pretrained representations, such as DINOv2-registers to bootstrap the learning signal and further improve upon them. This dense post-pretraining leads to superior performance across various models and datasets, despite requiring only 19 hours on a single GPU. This method generates high-quality dense feature encoders and establishes several new state-of-the-art results such as +5.5 % and +6% for non-parametric in-context semantic segmentation on ADE20k and Pascal VOC, +7.2% and +5.7% for linear segmentation evaluations on COCO-Things and -Stuff and improvements in the 3D understanding of multi-view consistency on SPair-71k, by more than 1.5%.