  Consider axisymmetric strong solutions of the incompressible Navier-Stokes
equations in $\R^3$ with non-trivial swirl. Let $z$ denote the axis of symmetry
and $r$ measure the distance to the z-axis. Suppose the solution satisfies
either $|v (x,t)| \le C_*{|t|^{-1/2}} $ or, for some $\e > 0$, $|v (x,t)| \le
C_* r^{-1+\epsilon} |t|^{-\epsilon /2}$ for $-T_0\le t < 0$ and $0<C_*<\infty$
allowed to be large. We prove that $v$ is regular at time zero.
