  We have performed Monte Carlo calculations of gamma-ray transport in models
of the clumpy debris cloud of the LMC supernova, SN1987A, to study the
influence of composition mixing and heterogeneity on its emergent gamma-ray and
X-ray fluxes. In particular, we have focused on the problematic Ginga band (16
-- 28 keV) flux at day 600, whose measured value was an order of magnitude
higher than predicted by previous theory. We find that the hydrogen of the
envelope could not have been intimately mixed with the heavy elements of the
core and that the hydrogen/helium volume filling factor interior to 4000 km/s
must have been large ($\ge 40\%$). A physical separation of the scattering
region and the regions occupied by the high-Z elements is required. The 600-day
models that best fit both the line data at 847 keV and 1238 keV and the
measured Ginga band fluxes suggest that as much as 50\% of the explosively
produced $^{56}$Ni stayed interior to 1000 km s$^{-1}$ and 2 M$_\odot$. The
$^{56}$Ni may have been more centrally-concentrated than in the benchmark
models. $^{56}$Ni filling factors greater than 60\% are not preferred, since
such models are too good at absorbing photons below 100 keV. Furthermore, a
total envelope mass between 10 $\mdot$ and 15 $\mdot$ is favored.
