Techniques for estimating and/or eliminating the effects of structure variations in the extragalactic radio sources used as fiducial points in 8.3-GHz geodetic VLBI observations are described and demonstrated. Particular attention is given to the data base statistics, the calibration of visibility data, the production of hybrid maps with AIPS, and the implementation of these steps in a software package. A set of X-band maps of 4C 39.25, obtained with the receivers of the Mark III dual-frequency VLBI network at six epochs during 1980-1985, is presented. Such maps are shown to be of value (1) for maintaining submarcsec accuracy in the extragalactic reference frame and (2) for qualitative astronomical monitoring of the sources. In 4C 39.25, for example, apparent superluminal motions, complex internal kinematics, and a double western component are observed.