One of the most promising approaches to unravelling the relationship between the optical and radio emission in AGN is to obtain nearly simultaneous optical polarization and VLBI polarization data. We present here such data for the three BL Lacertae objects 1147+245, 1418+546, and 1749+096 obtained during a λ = 6 cm VLBI polarization run at epoch 1992 March. In each of these three sources, the optical polarization position angle is aligned with the radio polarization position angle either in the VLBI core or in a VLBI jet component that is barely resolved from the core. Together with similar results presented earlier for an additional 4 BL Lacertae objects and the OVV quasar 3C 279, these results strongly indicate that the optical and radio polarized emission in these sources are linked to a much greater extent than has usually been expected. There is also a hint that the optical and VLBI degrees of polarization may be positively correlated, though more data are needed to confirm this. These results suggest that either the emission at these two frequencies is co-spatial or that the source geometry is quite uniform over long distances. The available data suggest that the strong optical polarization in these sources is associated with the formation and emergence of compact new VLBI components.