Accommodating intraocular (AIOL) assemblies for enabling post implantation in situ manual selective displacement of an AIOL along a human eye's visual axis relative to stationary anchor points. Axial displacement may be over a continuous range or alternatively at discrete axial stopping positions typically from about 100 μm to about 300 μm apart. Novels AIOLs designed to be at least partially folded for facilitating insertion into a human eye through a relatively small incision.