  Let $s$ denote West's stack-sorting map. A permutation is called
$t-\textit{sorted}$ if it is of the form $s^t(\mu)$ for some permutation $\mu$.
We prove that the maximum number of descents that a $t$-sorted permutation of
length $n$ can have is $\left\lfloor\frac{n-t}{2}\right\rfloor$. When $n$ and
$t$ have the same parity and $t\geq 2$, we give a simple characterization of
those $t$-sorted permutations in $S_n$ that attain this maximum. In particular,
the number of such permutations is $(n-t-1)!!$.
