  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.
