  We present the results of parsec-scale circular polarization (CP)
measurements based on VLBA data for a number of radio-bright, core-dominated
AGN obtained simultaneously at 15, 22 and 43 GHz. The degrees of CP $m_c$ for
the VLBI core region at 15 GHz are similar to values reported earlier at this
wavelength, with typical values of a few tenths of a percent.We find that $m_c$
as often rises as falls with increasing frequency between 15 and 22 GHz, while
$m_c$ at 43 GHz is in all cases higher than at 22 and 15 GHz. This behaviour
seems contrary to expectations, since the degree of CP from both synchrotron
radiation and Faraday conversion of linear to circular polarization should {\em
decrease} towards higher frequencies if the source is homogeneous. The increase
in $m_c$ at 43 GHz may be due to the presence of regions of both positive and
negative CP with different frequency dependences on small scales within the
core region; alternatively, it may be associated with the intrinsic
inhomogeneity of a Blandford-K\"onigl-like jet. In several objects, the
detected CO appears to be near, but not coincident with the core, although
further observations are needed to confirm this. We find several cases of
changes in sign with frequency, most often between 22 and 43 GHz. We find
tentative evidence for transverse structure in the CP of 1055+018 and
1334$-$127 that is consistent with their being generated by either the
synchrotron mechanism or Faraday conversion in a helical magnetic field. Our
results confirm the earlier finding that the sign of the CP at a given
observing frequency is generally consistent across epochs separated by several
years or more, suggesting stability of the magnetic field orientation in the
innermost jets.
