In this work we scrutinize a low level computer vision task - non-maximum suppression (NMS) - which is a crucial preprocessing step in many computer vision applications. Especially in real time scenarios, efficient algorithms for such preprocessing algorithms, which operate on the full image resolution, are important. In the case of NMS, it seems that merely the straightforward implementation or slight improvements are known. We show that these are far from being optimal, and derive several algorithms ranging from easy-to-implement to highly-efficient.