  New radial velocities of alpha 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 MSun and
0.934+/-0.0061 MSun 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
m/s 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.
