The optimized effective potential (OEP) method has been applied to convert 'traditional' non-local and non-multiplicative hybrid exchange-correlation potentials into local and multiplicative Kohn-Sham potentials. The latter have been evaluated in calculations of nuclear shielding constants for 22 small main-group molecules. The results obtained with local potentials are in much better agreement with experiment than those from their non-local counterparts. Exact-exchange admixture between 0.4 and 0.7 provides the best agreement with the experimental shielding constants. This should be contrasted to much lower exact-exchange admixture in a recent multiplicative Kohn-Sham procedure. With local hybrid potentials no coupling terms due to exact-exchange admixture have to be evaluated in the perturbational treatment. (C) 2004 Elsevier B.V. All rights reserved.