Summary: Currently, incremental algorithms may be seen as the lowest-cost computational methods to generate Delaunay tessellations in several point distributions. In this work, eight point-insertion sequences in incremental algorithms for generating Delaunay tessellations are evaluated. More specifically, four point-insertion sequences in incremental algorithms for generating Delaunay tessellations are proposed: with orders given by the red-black tree with in-order and level-order traversals, spiral ordering, and H-indexing. These four incremental algorithms with such sequences are compared with four incremental algorithms with point-insertion orders given by the following sequences: the Hilbert and Lebesgue curves, cut-longest-edge kd-tree, and random order. Six 2-D and seven 3-D point distributions are tested, with sets ranging from 25,000 to 8,000,000 points. The results of computational and storage costs of these eight algorithms are analyzed. It follows that the incremental algorithm with a point-insertion sequence in the order given by the cut-longest-edge kd-tree shows the lowest computational and storage costs of the sequences tested.