  We discuss the dynamics of dust grains subjected to uncompensated torques
arising from H_2 formation. In particular, we discuss grain dynamics when a
grain spins down and goes through a ``crossover''. As first pointed out by
Spitzer & McGlynn (1979), the grain angular momentum before and after a
crossover event are correlated, and the degree of this correlation affects the
alignment of dust grains by paramagnetic dissipation. We calculate the
correlation including the important effects of thermal fluctuations within the
grain material. These fluctuations limit the degree to which the grain angular
momentum J is coupled with the grain principal axis a_1 of maximal inertia. We
show that this imperfect coupling of a_1 with J plays a critical role during
crossovers and can substantially increase the efficiency of paramagnetic
alignment for grains larger than 10^{-5} cm. As a result, we show that for
reasonable choices of parameters, the observed alignment of $a\gtrsim 10^{-5}$
cm grains could be produced by paramagnetic dissipation in suprathermally
rotating grains, if radiative torques due to starlight were not present. We
also show that the efficiency of mechanical alignment in the limit of long
alignment times is not altered by the thermal fluctuations in the grain
material.
