Memory cells, and methods of forming such memory cells, are provided that include a steering element coupled to a carbon-based reversible resistivity switching material that has an increased resistivity, and a switching current that is less than a maximum current capability of the steering element used to control current flow through the carbon-based reversible resistivity switching material. In particular embodiments, methods and apparatus in accordance with this invention form a steering element, such as a diode, having a first cross-sectional area, coupled to a reversible resistivity switching material, such as aC, having a region that has a second cross-sectional area smaller than the first cross-sectional area.