Translating contact lenses which are truncated for correcting presbyopia and whose design is optimized to maximize translation ability while maintaining comfort when the lens is worn on eye. Truncation of the lenses results in a non-round geometry while still retaining under-lid residency in select portions of the lens itself. Maximum thickness and back surface radius of curvature along with ramp shape can be optimized individually or in combination to maximize translation of the lens relative to the eye, when the lens is positioned on eye.