VLBI observations from the POLARIS and Iris projects have been used to determine positions for 26 extragalactic radio sources. Nearly all the formal errors of the estimated coordinates are less than one millisecond of arc. Repeatability tests using subsets of the total data set indicate that systematic errors in the source coordinates are of the order of one half millisecond of arc. In order to attain submillisecond repeatability it was necessary to correct millisecond-level errors in the adopted IAU 1980 nutation model. Further improvements are expected as the number and distribution of VLBI baselines improve and as techniques are improved for eliminating atmospheric refraction effects. 21 references.