The theoretical complexity of vertex removal in a Delaunay triangulation is often given in terms of the degree d of the removed point with usual results O(d), O(d log d), or O(d²). In fact the asymptotic complexity is of poor interest since d is usually quite small. In this paper we carefully design code for small degrees 3 ≤ d ≤ 7, it improves the global behavior of the removal for random points by a factor of 2.