  From a microscopic model for the pyrochlore antiferromagnet Tb2Sn2O7,
including the crystal field Hamiltonian and interactions between the angular
momenta, we compute an effective pseudospin-1/2 Hamiltonian Heff$ that
incorporates perturbatively in the effective interactions the effect of excited
crystal field levels. We obtain the semiclassical ground states of Heff and
find a region of parameter space with a two-in/two-out spin ice configuration
on each tetrahedron with ordering wavevector q=0 and with spins canted away
from the local Ising axes as found in Tb2Sn2O7. This ground state can also be
obtained from a dipolar spin ice model in which the Ising constraint is
softened. Monte Carlo simulations on the latter model reveal a region of the
phase diagram with spin ice-like freezing and another with a transition into
Tb2Sn2O7-type long range order. We comment on the differences between Tb2Sn2O7
and the perplexing spin liquid Tb2Ti2O7.
