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 infrared Very Large Telescope 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 utilizing apparent H -band atomic absorption features and also discuss the general uncertainty of the system parameters of this well-studied object.