Context: The analysis of unresolved stellar populations demands evolutionary synthesis models with realistic physical ingredients and extended wavelength coverage. Aims: We quantitatively describe the first CO bandhead at 2.3 μm to allow stellar population models to provide improved predictions in this wavelength range. Methods: We observed a new stellar library with a better coverage of the stellar atmospheric parameter space than in earlier works. We performed a detailed analysis of the robustness of previous CO index definitions with spectral resolution, wavelength calibration, signal-to-noise ratio, and flux calibration. Results: We define a new line-strength index for the first CO bandhead at 2.3 μm, D_CO, better suited for stellar population studies than previous index definitions. We derive empirical fitting functions for the CO feature as a function of the stellar parameters (T_eff, log g and [Fe/H]), showing a detailed quantitative metallicity dependence.