New high-resolution spectroscopy of the Algol-type binary R CMa is presented and reduced, allowing a re-analysis of this 'puzzling' close pair. New radial velocity curves are in better agreement with the results of Glazunova, Yushchenko & Mrktichian, which revise upwards the relatively low masses of Tomkin. We find the following main parameters: M1= 1.67 ± 0.08, M2= 0.22 ± 0.07; R1= 1.78 ± 0.03, R2= 1.22 ± 0.07; L1= 8.2 ± 0.2, L2= 0.49 ± 0.01 (solar units); and photometric parallax 22±1 mas.Certain anomalous features of the system remain, however, in particular the combination of low period P and low mass ratio q. This may be related to the third body known to attend the close eclipsing pair, for which we also provide a new astrometric analysis and accompanying numerical results: M3= 0.8 ± 0.1; R3= 0.83 ± 0.07; L3= 0.4 ± 0.1 (solar units). The 'R CMa type', within the context of Algol evolution, may be seen as involving an unusually low q, P combination.