  Synthetic Lick indices (e.g. Mg_2, Fe, etc.) of Simple Stellar Population
(SSP) models are calibrated for the first time up to solar metallicity with a
sample of Milky Way globular clusters (GCs) which includes the metal rich GCs
of the Galactic bulge. This metallicity range is relevant to elliptical
galaxies. It is shown that the Bulge GCs and integrated light follow the same
correlation between Mg and Fe indices of elliptical galaxies, showing weaker Fe
indices at given Mg indices with respect to models that assume solar-scaled
abundances. This similarity is the robust empirical evidence for enhanced
alpha/Fe ratios in the stellar populations of elliptical galaxies, since the
globular clusters are independently known to be alpha-enhanced. The uniqueness
of this alpha-overabundance solution is checked by exploring the whole range of
model ingredients. We argue that the standard models reproduce the Mg-Fe
correlation at low metallicities because the stellar templates used in the
synthesis are the alpha-enhanced stars of the galactic Halo. These same models,
however, fail to recover the Mg-Fe pattern of Bulge clusters and ellipticals at
high metallicities because the high-metallicity templates are disk stars, which
are not alpha-enhanced. The new SSP models by Thomas, Maraston & Bender (2002)
which incorporate the dependence on alpha/Fe reproduce the Mg and Fe indices of
GCs at all metallicities, with alpha/Fe=+0.3, which is in agreement with
spectroscopic abundance determinations. The Balmer indices (Hbeta, Hdelta,
Hgamma) are very well calibrated, provided the Horizontal Branch morphology is
taken into account. In particular, we reproduce the Balmer lines of NGC 6388
and NGC 6441, which are metal-rich GCs with a tail of warm Horizontal Branch
stars. {Abridged}
