We present Very Long Baseline Array (VLBA) observations of the TeV blazars H
1426+428, 1ES 1959+650, and PKS 2155-304 obtained during the years 2001 through
2004. We observed H 1426+428 at four epochs at 8 GHz, and found that its
parsec-scale structure consisted of a ~17 mJy core and a single ~3 mJy jet
component with an apparent speed of 2.09 +/- 0.53c. The blazar 1ES 1959+650 was
observed at three epochs at frequencies of 15 and 22 GHz. Spectral index
information from these dual-frequency observations was used to definitively
identify the core of the parsec-scale structure. PKS 2155-304 was observed at a
single epoch at 15 GHz with dual-circular polarization, and we present the
first VLBI polarimetry image of this source. For 1ES 1959+650 and PKS 2155-304,
the current observations are combined with the VLBA observations from our
earlier paper to yield improved apparent speed measurements for these sources
with greatly reduced measurement errors. The new apparent speed measured for
component C2 in 1ES 1959+650 is 0.00 +/- 0.04c (stationary), and the new
apparent speed measured for component C1 in PKS 2155-304 is 0.93 +/- 0.31c. We
combine the new apparent speed measurements from this paper with the apparent
speeds measured in TeV blazar jets from our earlier papers to form a current
set of apparent speed measurements in TeV HBLs. The mean peak apparent pattern
speed in the jets of the TeV HBLs is about 1c. We conclude the paper with a
detailed discussion of the interpretation of the collected VLBA data on TeV
blazars in the context of current theoretical models for the parsec-scale
structure of TeV blazar jets.Comment: 16 pages, Astrophysical Journal, in pres