  Motivated by the low temperature magnetization curves of several spinel
chromites, we theoretically study classical mechanisms of degeneracy lifting in
pyrochlore antiferromagnets. Our main focus is on the coupling of spin exchange
to lattice distortions. Prior work by Penc et al. (Phys. Rev. Lett. 93, 197203
(2004)) has demonstrated that such coupling leads to a robust magnetization
plateau at half the saturation moment per spin, in agreement with experiment.
We show that a simple Einstein model incorporating local site distortions
generates a ``universal'' magnetic order on the plateau, and highlight the
distinct predictions of this model from that in Penc et al. (Phys. Rev. Lett.
93, 197203 (2004)). We also consider the complementary degeneracy-lifting
effects of further neighbor exchange interactions. We discuss the implications
for transitions off the plateau at both the high field and low field end, as
well as at fields close to the saturation value. We predict that under certain
circumstances there is spontaneous {\sl uniform} XY magnetization (transverse
to the field) for field values just above the plateau. These features may be
tested in experiments. While selecting a unique magnetic order in the half
magnetization plateau, at zero magnetic field the Einstein model retains an
extensive degeneracy, though significantly reduced compared with the pure
Heisenberg antiferromagnet.
