  We measured the radial-velocity curve of HD77581, the B-supergiant companion
of the X-ray pulsar Vela X-1, using 183 high-resolution optical spectra
obtained in a nine-month campaign. We derive radial-velocity amplitudes for
different lines and wavelength regions, and find all are consistent with each
other, as well as with values found in previous analyses. We show that one
apparent exception, an anomalously low value derived from ultra-violet spectra
obtained with the IUE, was due to an error in the analysis procedures. We
re-analyse all IUE spectra, and combine the resulting velocities with the ones
derived from the new optical spectra presented here, as well as those derived
from optical spectra published earlier. As in previous analyses, the radial
velocities show strong deviations from those expected for a pure Keplerian
orbit. The deviations likely are related to the pronounced line-profile
variations seen in our spectra. It turns out that systematic deviations as a
function of orbital phase are present. Our best estimate of the radial-velocity
amplitude, Kopt = 21.7 +/- 1.6 km/s, has an uncertainty not much reduced to
that found in previous analyses, in which the systematic deviations had not
been taken into account. Combining our velocity amplitude with the accurate
orbital elements of the X-ray pulsar, we infer M_ns sin^3i = 1.78 +/- 0.15
Msun.
