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Edge detection is a fundamental image analysis task that underpins numerous high-level vision applications. Recent advances in Transformer architectures have significantly improved edge quality by capturing long-range dependencies, but this often comes with computational overhead. Achieving higher pixel-level accuracy requires increased input resolution, further escalating computational cost and limiting practical deployment. Building on the strong representational capacity of recent Transformer-based edge detectors, we propose an Adaptive Multi-stage non-edge Pruning framework for Edge Detection(Amped). Amped identifies high-confidence non-edge tokens and removes them as early as possible to substantially reduce computation, thus retaining high accuracy while cutting GFLOPs and accelerating inference with minimal performance loss. Moreover, to mitigate the structural complexity of existing edge detection networks and facilitate their integration into real-world systems, we introduce a simple yet high-performance Transformer-based model, termed Streamline Edge Detector(SED). Applied to both existing detectors and our SED, the proposed pruning strategy provides a favorable balance between accuracy and efficiency-reducing GFLOPs by up to 40% with only a 0.4% drop in ODS F-measure. In addition, despite its simplicity, SED achieves a state-of-the-art ODS F-measure of 86.5%. The code will be released.