We measured the radial-velocity curve of HD 77581 , 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 International Ultraviolet Explorer , 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 , with root-mean-square amplitudes of \sim 7 ~ { } { km s ^ { -1 } } for strong lines of Si iv and N iii near 4100 Å , and up to \sim 20 ~ { } { km s ^ { -1 } } for weaker lines of N ii and Al iii near 5700 Å . The deviations likely are related to the pronounced line-profile variations seen in our spectra . Our hope was that the deviations would average out when a sufficient number of spectra were added together . It turns out , however , that systematic deviations as a function of orbital phase are present as well , at the 3 km s ^ { -1 } level , with the largest deviations occurring near inferior conjunction of the neutron star and near the phase of maximum approaching velocity . While the former might be due to a photo-ionisation wake , for which we observe direct evidence in the profiles of H \delta and H \alpha , the latter has no straightforward explanation . As a result , our best estimate of the radial-velocity amplitude , K _ { opt } = 21.7 \pm 1.6 km s ^ { -1 } , has an uncertainty not much reduced to that found in previous analyses , in which the influence of the systematic , phase-locked 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 ^ { 3 } { i } = 1.78 \pm 0.15 M _ { \odot } The tables in the Appendix are only available in electronic form at the CDS via anonymous ftp to cdsarc.u-strasbg.fr ( 130.79.128.5 ) or via http : //cdsweb.u-strasbg.fr/cgi-bin/qcat ? /A+A/ .