We present results from a series of follow-up observations of a subsample of the representative SAURON survey elliptical (E) and lenticular (S0) galaxies using the OASIS integral-field spectrograph. These observations focus on the central 10 " x 10 ", with roughly double the spatial resolution of the SAURON observations. This increased spatial resolution reveals a number of interesting and previously unresolved features in the measured stellar kinematics and absorption-line strengths. We find that galaxies exhibiting the youngest global stellar populations (as measured with SAURON) often contain a distinctly young central region (on scales of a few hundred parsec or less) compared to the rest of the galaxy. Moreover, these compact, young components are found to be mostly counter-rotating with respect to the rest of the galaxy. Given that there is no well-established reason for such young components to 'prefer' counter- over co-rotation, this finding raises the following questions: How common are these small KDCs as a function of age? Why are there more young than old compact KDCs? Where are the equivalent co-rotating components? We explore these questions using simple simulated velocity fields and stellar population models, and find that the fading of the young component as it evolves, coupled with the fact that counter-rotating components are more easily detected in the velocity field, may help explain the observed trends.