Keypoint detection usually results in a large number of keypoints which are mostly clustered, redundant, and noisy. These keypoints often require special processing like Adaptive Non-Maximal Suppression (ANMS) to retain the most relevant ones. In this paper, we present three new efficient ANMS approaches which ensure a fast and homogeneous repartition of the keypoints in the image. For this purpose, a square approximation of the search range to suppress irrelevant points is proposed to reduce the computational complexity of the ANMS. To further speed up the proposed approaches, we also introduce a novel strategy to initialize the search range based on image dimension which leads to a faster convergence. An exhaustive survey and comparisons with already existing methods are provided to highlight the effectiveness and scalability of our methods and the initialization strategy