Electron cooling of particle beams should offer a means for variable emittance control. Electron cooling works by superimposing a cold electron beam on a hot particle beam. Heat is transferred from the hot beam to the cold electron beam until an equilibrium is reached. The cold electron beam is continuously generated and discarded into a collector, allowing the minimum beam temperature to be obtained. The rate of cooling is determined by the cold electron beam current. If the cooling rate is too large, equilibrium emittances will be established that lead to instability. A low longitudinal emittance can lead to a susceptibility to the Z/n instability, while low transverse emittances may lead to space charge tune shifts that force a crossing of destructive betatron resonances. Control of the final emittance would enable an avoidance of these problems. In the absence of instabilities and under an ideal vacuum, equilibrium will be established between electron cooling and intrabeam scattering. Varying the electron cooling current will cause a change in the equilibrium emittance. Thus, a variable current electron cooling system can provide effective emittance control, allowing the emittance to be set to a value that is experimentally chosen as the best operating point for a given machine.