Using the near-infrared spectral stellar library of Cenarro et al. (J/MNRAS/326/959), the behaviour of the MgI line at 8807Å and nearby TiO bands is analyzed in terms of the effective temperature, surface gravity and metallicity of the library stars. New spectroscopic indices for both spectral features - namely MgI and sTiO - are defined, and their sensitivities to different signal-to-noise ratios, spectral resolutions, flux calibrations and sky emission-line residuals are characterized. The two new indices exhibit interesting properties. In particular, MgI is a good indicator of the Mg abundance, whereas sTiO is a powerful dwarf-to-giant discriminator for cold spectral types. Empirical fitting polynomials that reproduce the strength of the new indices as a function of the stellar atmospheric parameters are computed, and a fortran routine with the fitting function predictions is made available. A thorough study of several error sources, non-solar [Mg/Fe] ratios and their influence on the fitting function residuals is also presented. From this analysis, an [Mg/Fe] underabundance of ~-0.04 is derived for the Galactic open cluster M67. (2 data files).