Contact lenses and methods for designing and manufacturing contact lenses are disclosed. The contact lenses comprise a zone outside a central optic zone having a thickness profile with a varying thickness. The thickness profile provides rotational force to rotationally orient the contact lens when applied to a recipient eye. The thickness profile includes substantially curvilinear lines of constant thickness that extend generally horizontally across the lens. The curvilinear lines of substantially constant thickness may match the contact lines of the margins of at least one of the eyelids of the recipient.