  The dissipative infall of gas during the formation of a galaxy modifies the
density profile and shape of the dark halo. Gas dissipates energy radiatively
and sinks to the center of the dark halo forming the luminous part of a galaxy.
The resulting central density enhancement can alter the halo's orbital
distribution. We simulate dissipative infall inside of an initially triaxial
N-body dark halo by slowly growing a potential in the center of the particle
distribution. The dark halo transforms from a prolate-triaxial halo ($T \sim
0.8$) to an oblate-triaxial halo ($T \sim 0.5$) while approximately preserving
the flattening ($c/a \sim 0.5$). The main implication is that dark halos are
rounder and more oblate than previous predictions of purely collisionless
simulations with the new constraint that $b/a \gapp 0.7$. At the same time, the
distribution of intrinsic flattenings of dark halos ($\langle c/a \rangle =
0.5$, $\langle (c/a)^2 \rangle ^{1/2} = 0.15$) is preserved during the period
of baryonic infall. The oval distortions of disk galaxies should therefore be
slightly less than original predictions from collisionless dark halos. The
predicted distribution of shapes for dark halos from cosmological N-body
simulations is in better agreement with distribution of ellipticities of
elliptical galaxies if we assume all halos and galaxies become oblate-triaxial
in response to baryonic dissipation. The observed distribution of kinematic
misalignment angles is also consistent with this shape distribution if
