Since GRBs fade rapidly, it is important to publish accurate, precise positions at early times. For Swift-detected bursts, the best promptly available position is most commonly the X-ray Telescope (XRT) position. We present two processes, developed by the Swift team at Leicester, which are now routinely used to improve the precision and accuracy of the XRT positions reported by the Swift team. Both methods, which are fully automated, make use of a PSF-fitting approach which accounts for the bad columns on the CCD. The first method yields positions with 90% error radii <4.4″90% of the time, within 10-20 minutes of the trigger. The second method astrometrically corrects the position using UVOT field stars and the known mapping between the XRT and UVOT detectors, yielding enhanced positions with 90% error radii of <2.8″90% of the time, usually 2 hours after the trigger.