Exchange-correlation functionals are determined by constraining the potentials of flexible functional forms to be as parallel as possible to asymptotically vanishing ab initio exchange-correlation potentials. No thermochemical or gradient information is explicitly included in the fitting procedure. A range of spatial weightings is considered and the functionals are assessed by comparing with experiment and with the HCTH functional [J. Chem. Phys. 109, 6264 (1998)], which was determined by fitting to both potentials and to thermochemical and gradient data. Optimal thermochemistry, structures, and polarizabilities are simultaneously achieved by emphasizing an intermediate spatial region in the fit; an optimal functional is presented. The thermochemistry of this functional is less accurate than HCTH, although the structures of the fitting molecules are significantly improved. The mean absolute bond length error for 40 of the fitting molecules is 0.006 A, a factor of 2 improvement over HCTH. The bond lengths of 16 diatomic radicals absent from the fitting data are also improved. For the difficult molecules FOOF, FNO2, O-3, FO2, Cr(CO)(6), and Ni(CO)(4), the results are variable. The new functional improves the polarizabilities of 14 small molecules, compared to HCTH. It also improves electronic excitation energies to Rydberg states of N-2, H2CO, and C6H6, although the errors remain significant, reflecting the incorrect asymptotic potential. To obtain optimal nuclear shielding constants, it is necessary to emphasize regions closer to the nuclei; a second functional is presented which gives improved shieldings compared to HCTH. By considering the dominant occupied-virtual excitation contributions to the paramagnetic shieldings in CO and H2O, analogies are drawn between our results and those of a recently proposed method for improving density functional shielding constants. (C) 2001 American Institute of Physics.