  We calculate the effect of gravitational wave (gw) back-reaction on realistic
neutron stars (NS's) undergoing torque-free precession. By `realistic' we mean
that the NS is treated as a mostly-fluid body with an elastic crust, as opposed
to a rigid body. We find that gw's damp NS wobble on a timescale tau_{theta}
approx 2 x 10^5 yr [10^{-7}/(DId/I_0)]^2 (kHz/ nu_s)^4, where nu_s is the spin
frequency and DId is the piece of the NS's inertia tensor that "follows" the
crust's principal axis (as opposed to its spin axis). We give two different
derivations of this result: one based solely on energy and angular momentum
balance, and another obtained by adding the Burke-Thorne radiation reaction
force to the Newtonian equations of motion. This problem was treated long ago
by Bertotti and Anile (1973), but their claimed result is wrong. When we
convert from their notation to ours, we find that their tau_{theta} is too
short by a factor of order 10^5 for typical cases of interest, and even has the
wrong sign for DId negative. We show where their calculation went astray.
