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.

24 pages, 2 figures, submitted to ApJ, see also http://www.astro.princeton.edu/~library/prep.html