A systematic procedure for refining gradient corrections in Kohn-Sham exchange-correlation functionals is presented. The procedure is based on least-squares fitting to accurate thermochemical data. In this first application of the method, we use the G2 test set of Pople and co-workers to generate what we believe to be an optimum GGA/exact-exchange density-functional theory (i.e., generalized gradient approximation with mixing of exactly computed exchange). (C) 1997 American Institute of Physics. [S0021-9606(97)03444-2].