  Recent HST observations of the metal-rich bulge clusters NGC 6388 and NGC
6441 by Rich et al. (1997) have found that the horizontal branches (HBs) in
these clusters slope upward with decreasing B-V. Such an upward slope in the HB
morphology is not predicted by canonical HB models. Moreover, it cannot be
produced by either a greater cluster age or enhanced mass loss along the
red-giant branch (RGB). The peculiar HB morphology in these clusters may
provide an important clue for understanding the second-parameter effect.
  We have carried out extensive evolutionary calculations and numerical
simulations in order to understand the cause of the sloped HBs in NGC 6388 and
NGC 6441. Three scenarios have been investigated: i) A high cluster helium
abundance scenario, where the HB morphology is determined by long blue loops;
ii) A rotation scenario, where the core mass in the HB models is increased by
internal rotation during the HB phase; iii) A helium-mixing scenario, where
deep mixing on the RGB enhances the envelope helium abundance.
  All three of these scenarios predict sloped HBs with anomalously bright RR
Lyrae variables. We compare this prediction with the properties of the two
known RR Lyrae variables in NGC 6388 as well as with the properties of the
metal-rich field RR Lyrae variables and V9 in 47 Tuc.
