  In this article, we investigate the set of $\gamma$-sortable elements,
associated with a Coxeter group $W$ and a Coxeter element $\gamma\in W$, under
Bruhat order, and we denote this poset by $\mathcal{B}_{\gamma}$. We show that
this poset belongs to the class of SB-lattices recently introduced by Hersh and
M\'esz\'aros, by proving a more general statement, namely that all
join-distributive lattices are SB-lattices. The observation that
$\mathcal{B}_{\gamma}$ is join-distributive is due to Armstrong. Subsequently,
we investigate for which finite Coxeter groups $W$ and which Coxeter elements
$\gamma\in W$ the lattice $\mathcal{B}_{\gamma}$ is in fact distributive. It
turns out that this is the case for the "coincidental" Coxeter groups, namely
the groups $A_{n},B_{n},H_{3}$ and $I_{2}(k)$. We conclude this article with a
conjectural characteriziation of the Coxeter elements $\gamma$ of said groups
for which $\mathcal{B}_{\gamma}$ is distributive in terms of forbidden
orientations of the Coxeter diagram.
