As main-sequence stars do not produce carbon, the newly recognized class of carbon-rich dwarf (dC) stars is most easily explained if dC's are main-sequence bystanders polluted by mass transfer from a giant companion that has since become a white dwarf. We analyze intermediate (almost-equal-to 2 angstrom) resolution spectra of six dC's to constrain their radial velocities and abundances and to place them in context with other known or suspected mass-transfer binary (MTB) systems. We find that barium is enhanced in all dC's observed. Carbon isotope ratios appear to span a wide range in our sample, with C-13 often as strong as in the C-13-rich '' J '' stars. Both these abundance patterns are reminiscent of the CH stars, which are now accepted to be MTB systems. Wihin our velocity resolution, we find no evidence for radial velocity (RV) variability. This is consistent with the RV variations observed in wide binary systems like CH stars, but not with close post-common-envelope white dwarf + red dwarf systems. We suggest that dC's are the main-sequence progenitors of CH giants and/or that CH giants are the high-luminosity tail in a distribution of MTB systems numerically dominated by dC's. Two recently discovered composite-spectrum DA/dC systems are also examined. The brighter DA/dC, PG 0824 + 289, has shown evidence for variable Balmer line emission, but has a previously unresolved close neighbor. We find that the neighbor is an unrelated M dwarf, so that the emission must arise from the DA/dC system. We examine two possible causes of the emission-chromospheric activity intrinsic to the dC, or reprocessing in a close binary of the DA's UV flux on the dC atmosphere.