During the last 3 years under the High Altitude Large Optics (HALO) Technology Program, we have been developing computer-controlled, optical surfacing technology for application to the manufacture of large lightweight, odd-shaped, infrared-quality aspheric mirrors that will be needed in the next generation of space telescopes. The program has consisted of developmental work on our small optical surfacing machine, to support on-going production of a large oblong demonstration mirror with our large machine. The problems addressed have been the measurement of the aspheric surface, the material removal model, the data reduction machine control algorithm, and lap designs for producing aspherics rapidly. To date, flats and spheres have been produced with rigid laps, control of absolute sag to 0.1 μm has been demonstrated, and a compliant lap concept has been developed. Controllability of this lap has been verified in polishing. The proof test, to start shortly, will be a full grind/ polish fabrication sequence to produce an eccentric ellipse. The program plan calls for later fabrication of a large two-panel eccentric ellipse, using the present large oblong demonstration mirror as the inner panel. A new concept for a self-calibrating, absolute measuring machine is being developed for use in the production of the large ellipse. It should be accurate enough for all of the grinding and perhaps for the polishing and final figuring too.