We investigate the relationship between R Coronae Borealis (RCB) stars and hydrogen-deficient carbon (HdC) stars by measuring precise 16O/18O ratios for five cool RCB stars. The 16O/18O ratios are derived by spectrum synthesis from high-resolution (R ~ 50, 000) K-band spectra. Lower limits to the 16O/17O and 14N/15N ratios as well as Na and S abundances (when possible) are also given. RCB stars in our sample generally display less 18O than HdC stars—the derived 16O/18O ratios range from 3 to 20. The only exception is the RCB star WX CrA, which seems to be an HdC-like star with 16O/18O = 0.3. Our result of a higher 16O/18O ratio for the RCB stars must be accounted for by a theory of the formation and evolution of HdC and RCB stars. We speculate that a late dredge-up of products of He burning, principally 12C and 16O, may convert an 18O-rich HdC star into an 18O-poor RCB star as the H-deficient star begins its final evolution from a cool supergiant to the top of the white dwarf cooling track.