  We present models that predict spectra of old- and intermediate-aged stellar
populations at 2.51\AA\ (FWHM) with varying [\alpha/Fe] abundance. The models
are based on the MILES library and on corrections from theoretical stellar
spectra. The models employ recent [Mg/Fe] determinations for the MILES stars
and BaSTI scaled-solar and \alpha-enhanced isochrones. We compute models for a
suite of IMF shapes and slopes, covering a wide age/metallicity range. Using
BaSTI, we also compute "base models" matching The Galactic abundance pattern.
We confirm that the \alpha-enhanced models show a flux excess with respect to
the scaled-solar models blue-ward $\sim$4500\AA, which increases with age and
metallicity. We also confirm that both [MgFe] and [MgFe]' indices are
[\alpha/Fe]-insensitive. We show that the sensitivity of the higher order
Balmer lines to [\alpha/Fe] resides in their pseudo-continua, with narrower
index definitions yielding lower sensitivity. We confirm that the
\alpha-enhanced models yield bluer (redder) colours in the blue (red) spectral
range. To match optical colours of massive galaxies we require both
\alpha-enhancement and a bottom-heavy IMF. The comparison of Globular Cluster
line-strengths with our predictions match the [Mg/Fe] determinations from their
individual stars. We obtain good fits to both full spectra and indices of
galaxies with varying [\alpha/Fe]. Using thousands of SDSS galaxy spectra we
obtain a linear relation between a proxy for the abundance, [Z$_{\rm
Mg}$/Z$_{\rm Fe}$]$_{\rm SS(BaSTI)}$, using solely scaled-solar models and the
[Mg/Fe] derived with models with varying abundance ([Mg/Fe]=0.59[Z$_{\rm
Mg}$/Z$_{\rm Fe}$]$_{\rm SS(BaSTI)}$). Finally we provide a user-friendly,
web-based facility, which allows composite populations with varying IMF and
[\alpha/Fe] ( http://miles.iac.es ).
