  We consider permutations of $\{1,...,n\}$ obtained by
$\lfloor\sqrt{n}t\rfloor$ independent applications of random stirring. In each
step the same marked stirring element is transposed with probability $1/n$ with
any one of the $n$ elements. Normalizing by $\sqrt{n}$ we describe the
asymptotic distribution of the cycle structure of these permutations, for all
$t\ge 0$, as $n\to\infty$.
