Consider axisymmetric strong solutions of the incompressible Navier-Stokes equations in 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, for some 0 ≤ ε ≤ 1, |v (x, t)| ≤ C_* r^-1+ε |t|^-ε/2 for - T₀ ≤ t < 0 and 0 < C_* < ∞ allowed to be large. We prove that v is regular at time zero.