1. A method for making a memory cell, comprising: forming a dielectric support layer over a bottom electrode, the dielectric support layer having an upper surface; forming a cavity through the dielectric support layer; exposing a surface of the bottom electrode and defining a dielectric support structure having a sidewall; forming a film of memory material over the dielectric support structure and in the cavity; depositing a dielectric spacer layer over the memory material film; forming a dielectric sidewall spacer from the dielectric spacer layer and a memory material structure having a generally horizontal portion underlying the dielectric sidewall spacer and a generally vertical portion between the dielectric sidewall spacer and the sidewall of the dielectric support structure; forming a dielectric fill; planarizing the dielectric fill to expose upper ends of the vertical portion of the memory material structure; forming a memory material layer over the planarized dielectric fill; depositing a top electrode material over the memory material layer; and forming a top electrode from the top electrode material and a memory material element from the memory material structure.