This article presents a context-aware tracing strategy (CATS) for crisp edge detection with deep edge detectors, based on an observation that the localization ambiguity of deep edge detectors is mainly caused by the mixing phenomenon of convolutional neural networks: Feature mixing in edge classification and side mixing during fusing side predictions. The CATS consists of two modules: A novel tracing loss that performs feature unmixing by tracing boundaries for better side edge learning, and a context-aware fusion block that tackles the side mixing by aggregating the complementary merits of learned side edges. Experiments demonstrate that the proposed CATS can be integrated into modern deep edge detectors to improve localization accuracy. With the vanilla VGG16 backbone, in terms of BSDS500 dataset, our CATS improves the F-measure (ODS) of the RCF and BDCN deep edge detectors by 12 and 6 percent, respectively when evaluating without using the morphological non-maximal suppression scheme for edge detection.