Recent Hubble Space Telescope observations have found that the horizon
tal branches (HBs) in the metal-rich globular clusters NGC 6388 and NG
C 6441 slope upward with decreasing B - V. Such a slope is not predict
ed by canonical HE models and cannot be produced by either a greater c
luster age or enhanced mass loss along the red giant branch (RGB). The
peculiar HE morphology in these clusters may provide an important clu
e for understanding the second-parameter effect. We have carried out e
xtensive evolutionary calculations and numerical simulations in order
to explore three noncanonical scenarios for explaining the sloped HBs
in NGC 6388 and NGC 6441: (1) a high cluster helium abundance scenario
, in which the HE evolution is characterized by long blue loops; (2) a
rotation scenario, in which internal rotation during the RGB phase in
creases the HE core mass; and (3) a helium-mixing scenario, in which d
eep mixing on the RGB enhances the envelope helium abundance. All thre
e of these scenarios predict sloped HBs with anomalously bright RR Lyr
ae variables. We compare this prediction with the properties of the tw
o known RR Lyrae variables in NGC 6388. Additional observational tests
of these scenarios are suggested.