Enantioselective allylic oxidation of olefins with various peresters, using a catalytic amount of Cu(I)-pybox complex, can be tuned to achieve high asymmetric induction (up to 98% ee) by choosing a unique combination of a ligand and a perester at room temperature. The asymmetric induction in the reaction strongly depends on the nature of the substituents attached to the aryl ring of peresters. The presence of a gem-diphenyl group at C-5 and secondary or tertiary alkyl substituents at the chiral center (C-4) of the oxazoline rings is crucial for high enantioselectivity. A pi-pi stacking model has been proposed and discussed to explain the stereochemical outcome of the reaction.