An accommodating intraocular lens implant is provided that includes (a) a bowl-shaped posterior component and (b) an anterior component, which includes an anterior floating lens unit, which includes an anterior lens; a circumferential rim; and levers, which connect the anterior floating lens unit to the circumferential rim, such that the anterior floating lens unit is movable toward and away from the circumferential ring in an anterior-posterior direction. The bowl-shaped posterior component and the anterior component are distinct from each other and not permanently fixed to each other, and are shaped so as to be assemblable together in situ in a human eye such that the circumferential rim contacts an interface region of an inner surface of the bowl-shaped posterior component, and the levers are pivotable about the interface region during motion of the anterior floating lens unit toward and away from the circumferential ring in the anterior-posterior direction.