An accommodating intraocular lens construction includes a lens of fixed optical power to correct refractive error and a lens of variable power to restore accommodation of the eye, which variable lens can have two optical elements which either shift perpendicular to the optical axis, or which variable lens can have two elements which move along the optical axis. The accommodating intraocular lens has at least one haptic to provide transfer of movement to at least one of the optical elements and at least one additional haptic for sulcus fixation to provide limitation of movement of at least one component of the lens along the optical axis. The movement of the additional haptic is largely independent from the haptic for movement.