  Let SU(r,d) be the moduli space of rank r, degree d vector bundles over a
smooth projective curve of genus $g\ge 2$. If (r,d)=1 and d divides r+1, then
SU is rational. Furthermore, if $0<\delta < r$ and all prime divisors of
$\delta$ divide r, and if d divides $r-\delta$, then SU is rational. The proof
is a variation on a result of Newstead and modifications due to Ballico and
then Boden and Yokogawa.
