New radial velocities of α Cen A & B obtained in the framework the Anglo-Australian Planet Search programme as well as in the CORALIE programme are added to those by Endl et al. (2001) to improve the precision of the orbital parameters. The resulting masses are 1.105 ± 0.0070 M⊙ and 0.934 ± 0.0061 M⊙ for A and B respectively. The factors limiting how accurately these masses can be derived from a combined visual-spectroscopic solution are investigated. The total effect of the convective blueshift and the gravitational redshift is also investigated and estimated to differ by 215 ± 8 ms-1 between the components. This suggests that the difference in convective blueshift between the components is much smaller than predicted from current hydrodynamical model atmosphere calculations. ; SCOPUS: ar.j ; info:eu-repo/semantics/published