Unitary accommodating intraocular lenses (AIOLs) including a haptics system for self-anchoring in a human eye's ciliary sulcus and a resiliently elastically compressible shape memory optical element having a continuously variable Diopter strength between a first Diopter strength in a non-compressed state and a second Diopter strength different than its first Diopter strength in a compressed state. The unitary AIOLS include an optical element with an exposed trailing surface and are intended to be used with a discrete base member for applying an axial compression force against the exposed trailing surface from a posterior direction. Some unitary AIOLs are intended to be used with either a purpose designed base member or a previously implanted standard in-the-bag IOL. Other unitary AIOLs are intended to be solely used with a purpose designed base member.