  Conjecturally, the only knots in $S^3$ with non-integer surgeries producing
Seifert fibered spaces are torus knots and cables of torus knots. In this
paper, we make progress on the associated realization problem. Let $Y$ be a
small Seifert fibered space arising by $p/q$-surgery on a knot in $S^3$, where
$p/q$ is positive and a non-integer. Let $e$ denote the weight of the central
vertex in the minimal star-shaped plumbing that $Y$ bounds. We show that if
$e\leq -2$ or $e\geq 3$, then $Y$ can be obtained by $p/q$-surgery on a torus
knot or a cable of a torus knot.
