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In recent years nonuniform dipoles with bending-radius variation have been studied for reducing storage ring emittance. According to a new minimum-emittance theory, the effects of an arbitrary dipole can be characterized with two parameters determined by the dipole. To have a better idea of the potentials of nonuniform dipoles, here we numerically explore the possible values of these two parameters and associated bending profiles for optimal emittance reduction. Such optimization results provide a useful reference for lattice designs involving nonuniform bending. Simple bending-radius profiles (a short segment of constant radius with linear ramps on the sides) were found to be close to the optimal. Basic beam and lattice properties such as emittance, energy spread, and phase advances are presented based on the optimal dipole solutions.