We have used the Very Long Baseline Array (VLBA) and the Very Large Array (
VLA) to image Galactic neutral hydrogen in absorption toward four compact e
xtragalactic radio sources with a resolution of 10 mas. Previous VLBA data
published by Faison et al. have shown the existence of prominent structures
in the direction of the extragalactic source 3C 138 with scale sizes of 10
-20 AU and changes in H I optical depth in excess of 0.8 +/- 0.1. We confir
m the small-scale H I optical depth variations toward 3C 147 suggested earl
ier at a level up to 20% +/- 5%. The sources 3C 119, CJ1 2352 + 495, and CJ
1 0831 + 557 show no significant change in H I optical depth across the sou
rces with 1 sigma limits of 30%, 50%, and 100%. Of the seven sources recent
ly investigated with the VLBA and VLA, only 3C 138 and 3C 147 show statisti
cally significant variations in H I opacities. Deshpande and collaborators
have attempted to explain the observed small-scale structures as extensions
of the observed power spectra of structures on parsec-size scales. The pre
dictions by Deshpande are consistent with the VLBA H I data observed in the
directions of a number of sources, including 3C 147, but they are not cons
istent with our previous observations of the H I opacity structure toward 3
C 138.