  GRS 1915+105 has the largest mass function of any Galactic black hole system,
although the error is relatively large. Here we present spectroscopic analysis
of medium-resolution IR VLT archival data of GRS 1915+105 in the K-band. We
find an updated ephemeris, and report on attempts to improve the mass function
by a refinement of the radial velocity estimate. We show that the spectra are
significantly affected by the presence of phase-dependent CO bandhead emission,
possibly originating from the accretion disc: we discuss the impact this has on
efforts to better constrain the black hole mass. We report on a possible way to
measure the radial velocity utilising apparent H-band atomic absorption
features and also discuss the general uncertainty of the system parameters of
this well-studied object
