  Collisions of polar $^{1}\Sigma$ state molecules at ultralow energies are
considered, within a model that accounts for long-range dipole-dipole
interactions, plus rotation of the molecules. We predict a substantial
suppression of dipole-driven inelastic collisions at high values of the applied
electric field, namely, field values of several times $B_e/\mu$. Here $B_e$ is
the rotational constant, and $\mu$ is the electric dipole moment of molecules.
  The sudden large drop in the inelastic cross section is attributed to the
onset of degeneracy between molecular rotational levels, which dramatically
alters the scattering Hamiltonian. As a result of the large ratio of elastic to
inelastic collision rates, we predict that evaporative cooling may be feasible
for $^{1}\Sigma$ state molecules in weak-field-seeking states, provided a large
bias electric field is present.
