  We investigate the predicted Color-Magnitude distribution of metal-rich
Horizontal Branch (HB) stars, discussing selected theoretical models computed
under various assumptions about the star metallicity and the efficiency of
super-adiabatic convection. We find that canonical Zero Age Horizontal Branches
with metallicity larger or of the order of Z=0.002 should be all affected by a
tilt, by an amount which increases when the metallicity is increased and/or the
mixing length is decreased, reaching a tilt of $\Delta V \sim$0.2 mag in the
case of solar metallicity when a mixing length value $\alpha$=1.6 is assumed
($\Delta V$ is the magnitude difference between the top of the blue HB and the
fainter magnitude reached by the red HB). Uncertainties in the luminosity of
the red HB due to uncertainty in the mixing length value are discussed. We
finally discuss the much larger tilt observed in the clusters NGC 6441 and NGC
6388, reporting additional evidence against suggested non-canonical
evolutionary scenarios. Numerical experiments show that differential reddening
could produce such sloped HBs. Further, HST-PC imaging of NGC 6441 gives clear
indications about the occurrence of differential reddening across the cluster.
However, the same imaging shows that the observed slope of the red HB {\em is
not} an artifact of differential reddening. We finally show that sloping red
HBs in metal rich clusters are a common occurrence not necessarily correlated
with the appearance of extended blue HB.
