Under one aspect, a covered nanotube switch includes: (a) a nanotube element including an unaligned plurality of nanotubes, the nanotube element having a top surface, a bottom surface, and side surfaces; (b) first and second terminals in contact with the nanotube element, wherein the first terminal is disposed on and substantially covers the entire top surface of the nanotube element, and wherein the second terminal contacts at least a portion of the bottom surface of the nanotube element; and (c) control circuitry capable of applying electrical stimulus to the first and second terminals. The nanotube element can switch between a plurality of electronic states in response to a corresponding plurality of electrical stimuli applied by the control circuitry to the first and second terminals. For each different electronic state, the nanotube element provides an electrical pathway of different resistance between the first and second terminals.