  The outer-halo globular cluster NGC 6229 has a peculiar horizontal-branch
(HB) morphology, with clear indications of a bimodal HB and a ``gap" on the
blue HB. In this paper, we present extensive synthetic HB simulations to
determine whether peculiar distributions in the underlying physical parameters
are needed to explain the observed HB morphology. We find that a unimodal mass
distribution along the HB can satisfactorily account for the observed HB
bimodality, *provided* the mass dispersion is substantially larger than usually
inferred for the Galactic globular clusters. In this case, NGC 6229 should have
a well-populated, extended blue tail. A truly bimodal distribution in HB masses
can also satisfactorily account for the observed HB morphology, although in
this case the existence of an extended blue tail is not necessarily implied.
The other two well-known bimodal-HB clusters, NGC 1851 and NGC 2808, are
briefly analyzed. While the HB morphology of NGC 1851 can also be reproduced
with a unimodal mass distribution assuming a large mass dispersion, the same is
not true of NGC 2808, for which a bimodal, and possibly multimodal, mass
distribution seems definitely required.
  The problem of gaps on the blue HB is also discussed. Applying the standard
Hawarden (1971) and Newell (1973) chi-squared test, we find that the NGC 6229
gap is significant at the 99.7% level. However, in a set of 1,000 simulations,
blue-HB gaps comparable to the observed one are present in ~ 6 - 9% of all
cases. We employ a new and simple formalism, based on the binomial
distribution, to explain the origin of this discrepancy, and conclude that
Hawarden's method, in general, substantially overestimates the statistical
significance of gaps.
