We are surveying eight nearby Seyfert galaxies (four Sy1s and four Sy2s) that have compact radio cores, using the VLBA. We are interested in parsec-scale morphology and low-frequency absorption effects, and so are observing four frequencies (1.6, 4.8, 8.4 and 15 GHz) to get spectral-index diagnostics. In this paper, we present results on two galaxies, NGC 1068 and NGC 4151. NGC 4151 shows a curved radio jet on the sub-parsec scale, with the smallest scale structure misaligned by 55° from the jet on scales of parsecs to hundreds of parsecs. NGC 1068 contains several components in the inner tens of parsecs, with those components showing a variety of absorption and resolution effects.