The High Resolution Dynamics Limb Sounder (HIRDLS) instrument was launched on NASA's Aura spacecraft on 15 July 2004. When activation was completed 25 days later, it was discovered that the measured radiances were very different from those that were expected. After a long series of analyses and diagnostic tests, the cause was confirmed to be a blockage that covers much of the front aperture, preventing even one completely clear view of the atmosphere. In this paper the steps required to correct the radiances for the effects of the blockage are noted. These are calibrating the radiances, removing the effects of the blockage oscillating, and the radiance coming from the blockage, correcting for the effects of the partial aperture, and filtering the noise. The paper describes the algorithms needed, and presents the results of their application. The success of the procedures will be demonstrated by the quality of the resulting radiances and retrieved profiles of temperature and trace species. The difficulties that have been eliminated, and that still remain are noted, along with plans for further improvement. Finally, the scientific implications are briefly discussed.