  We present differential stellar population models, which allow improved
determinations of the ages, iron and alpha-element abundances of old stellar
populations from spectral fitting. These new models are calibrated at solar
abundances using the predictions from classical, semi-empirical stellar
population models. We then use the predictive power of fully synthetic models
to compute predictions for different [Fe/H] and [alpha/Fe]. We show that these
new differential models provide remarkably accurate fits to the integrated
optical spectra of the bulge globular clusters NGC6528 and NGC6553, and that
the inferred [Fe/H] and [alpha/Fe] agree with values derived elsewhere from
stellar photometry and spectroscopy. The analysis of a small sample of SDSS
early-type galaxies further confirms that our alpha-enhanced models provide a
better fit to the spectra of massive ellipticals than the solar-scaled ones.
Our approach opens new opportunities for precision measurements of abundance
ratios in galaxies.
