  Let $W$ be an irreducible Coxeter group. We define the Coxeter
pop-stack-sorting operator $\mathsf{Pop}:W\to W$ to be the map that fixes the
identity element and sends each nonidentity element $w$ to the meet of the
elements covered by $w$ in the right weak order. When $W$ is the symmetric
group $S_n$, $\mathsf{Pop}$ coincides with the pop-stack-sorting map.
Generalizing a theorem about the pop-stack-sorting map due to Ungar, we prove
that \[\sup\limits_{w\in W}\left|O_{\mathsf{Pop}}(w)\right|=h,\] where $h$ is
the Coxeter number of $W$ (with $h=\infty$ if $W$ is infinite) and $O_f(w)$
denotes the forward orbit of $w$ under a map $f$. When $W$ is finite, this
result is equivalent to the statement that the maximum number of terms
appearing in the Brieskorn normal form of an element of $W$ is $h-1$. More
generally, we define a map $f:W\to W$ to be compulsive if for every $w\in W$,
$f(w)$ is less than or equal to $\mathsf{Pop}(w)$ in the right weak order. We
prove that if $f$ is compulsive, then $\sup\limits_{w\in W}|O_f(w)|\leq h$.
This result is new even for symmetric groups.
  We prove that $2$-pop-stack-sortable elements in type $B$ are in bijection
with $2$-pop-stack-sortable permutations in type $A$, which were enumerated by
Pudwell and Smith. Claesson and Gudmundsson proved that for each fixed
nonnegative integer $t$, the generating function that counts
$t$-pop-stack-sortable permutations in type $A$ is rational; we establish
analogous results in types $B$ and $\widetilde A$.
