Lithographically fabricated point contacts serve as important examples of mesoscopic conductors, as electrodes for molecular electronics, and as ultra-sensitive transducers for mechanical motion. We have developed a reproducible technique for fabricating metallic point contacts though electromigration. We employ fast analog feedback in a four-wire configuration in combination with slower computer controlled feedback to avoid catastrophic instability. This hybrid system allows electromigration to proceed while dissipating approximately constant power in the wire. We are able to control the final resistance of the point contact precisely below 5 k\Omega\ and to within a factor of three when the target resistance approaches 12 k\Omega\ where only a single conducting channel remains.
