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 superadiabatic convection. We find that canonical zero-age horizontal branches with metallicity larger or of the order of Z = 0.002 should all be affected by a tilt by an amount that increases when the metallicity is increased and/or the mixing length is decreased, reaching a tilt of DeltaV similar to0.2 mag in the case of solar metallicity when a mixing-length value alpha = 1.6 is assumed (DeltaV 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 noncanonical evolutionary scenarios. Numerical experiments show that differential reddening could produce such sloped HBs. Furthermore, Hubble Space Telescope planetary- camera imaging of NGC 6441 gives clear indications of the occurrence of differential reddening across the cluster. However, the same imaging shows that the observed slope of the red HB 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 HBs.