This paper gives a procedure to control the size variation in a mesh adaption scheme where the size speci cation (the so-called control space) is used to govern the mesh generation stage. The method consists in replacing the initial control space by a reduced one by means of size or metric. It allows to improve, a priori, the quality of the adapted mesh and to speed up the adaption procedure. Several numerical examples show the e ciency of the reduction scheme. ? 1998 John Wiley & Sons, Ltd.