  We present SMA and CARMA continuum and spectral line observations of five
dense cores located in the Perseus and Ophiuchus molecular clouds whose masses
exceed their thermal Jeans masses. Three of these cores have previously been
identified as being starless and two have been classified as being possibly
protostellar. We find that one core is certainly protostellar. The other four
cores, however, are starless and undetected in both C18O (2-1) and 1.3mm
continuum emission. These four starless cores have flat density profiles out to
at least 0.006 pc, which is typical for starless cores in general. Density
profiles predicted by some collapse models, especially in the early stages of
infall, are consistent with our observations. Archival data reveal that these
starless cores have significant non-thermal support against collapse, although
they may still be unstable.
