  We demonstrate that the rapidity and robustness of slow contraction in
homogenizing and flattening the universe found in simulations in which the
initial conditions were restricted to non-perturbative variations described by
a single fourier mode along only a single spatial direction are in general
enhanced if the initial variations are along two spatial directions, include
multiple modes, and thereby have reduced symmetry. Particularly significant are
shear effects that only become possible when variations are allowed along two
or more spatial dimensions. Based on the numerical results, we conjecture that
the counterintuitive enhancement occurs because more degrees of freedom are
activated which drive spacetime away from an unstable Kasner fixed point and
towards the stable Friedmann-Robertson-Walker fixed point.
