After 16 years of radial-velocity observations of a sample of 22 R-type carbon stars, no evidence for binary motion has been detected in any of them. This is surprising considering that approximately 20% of normal late-type giants are spectroscopic binaries, and the fraction is close to 100% in barium, CH, and subgiant/dwarf CH and barium stars. It is suggested, therefore, that a process that has caused the mixing of carbon to the surface of these stars cannot act in a wide binary system. Possibly, the R stars were once all binaries, but with separations that would not allow them to evolve completely up the giant and asymptotic giant branchs without coalescing. This coalescence may be the agent which causes carbon produced in the helium-core flash to be mixed outwards to a region where convection zones can bring it to the surface of the star.

11 Latex pages plus 4 ps figures, (accepted by PASP) Also available at http://www.hia.nrc.ca/eprint.html