Randomized incremental constructions are widely used in computational geometry, but they perform very badly on large data because of their inherently random memory access patterns. We define a biased randomized insertion order which removes enough randomness to significantly improve performance, but leaves enough randomness so that the algorithms remain theoretically optimal. Categories and Subject Descriptors F.2.2 [Theory of Computation]: Analysis of Algorithms and Problem Complexity—Geometrical problems and computations General Terms Algorithms Keywords Randomized incremental construction, Delaunay triangulation, virtual memory.