Robust registration of two 3-D point sets is a common problem in computer vision. The Iterative Closest Point (ICP) algorithm is undoubtedly the most popular algorithm for solving this kind of problem. In this paper, we present the Picky ICP algorithm, which has been created by merging several extensions of the standard ICP algorithm, thus improving its robustness and computation time. Using pure 3-D point sets as input data, we do not consider additional information like point color or neighborhood relations. In addition to the standard ICP algorithm and the Picky ICP algorithm proposed in this paper, a robust algorithm due to Masuda and Yokoya and the RICP algorithm by Trucco et al. are evaluated. We have experimentally determined the basin of convergence, robustness to noise and outliers, and computation time of these four ICP based algorithms.