  Let $K= K(w,b,t)$ be a 1-bridge braid in a solid torus $V$, and let $\gamma$
be a $(p,q)$ curve on the torus $T = \partial V$ of the exterior $M_K$ of $K$.
It will be shown that Dehn filling on $T$ along $\gamma$ produces a solid torus
if and only if $p$ and $q$ satisfy one of four conditions determined by the
parameters $(w,b,t)$ of the knot $K$. This solves the classification problem
raised by Menasco and Zhang for such Dehn fillings.
