We expand our previous studies of the parsec-scale structure of TeV blazars by presenting firstepoch images from VLBA monitoring of ten newer TeV HBLs. All ten sources were successfully detected and imaged, and all showed a one-sided core-jet structure. Many display a morphology common to TeV HBLs: a short, collimated jet followed by a transition to low surface brightness extended emission with a much broader opening angle. The newly detected TeV HBLs tend to be fainter in the radio; the median core flux density was 22 mJy, and the median brightness temperature was 8 × 109 K. The brightness temperatures are well below the equipartition limit, and thus the VLBI cores do not require strong beaming, consistent with the modest values of Doppler and Lorentz factors found in the VLBI jets of TeV HBLs by other studies, and contrasting with the strong beaming generally required by the TeV emission. We study the full sample of TeV HBLs that have been observed with VLBI, and find a correlation between TeV flux and VLBI core brightness temperature, suggesting different but correlated beaming factors for the TeV and radio emission. We present a discussion of these observations in the context of velocity structures in the jets of the TeV HBLs.