  We study axially symmetric $D$-solutions of three dimensional steady
Navier-Stokes equations. We prove that if the velocity $u$ decays like
$|x'|^{-(\frac{2}{3})^+}$ uniformly for $z$, or the vorticity $\omega$ decays
like $|x'|^{-(\frac{5}{3})^+}$ uniformly for $z$, then $u$ vanishes. Here
$|x'|$ denotes the distance to the axis.
