  In all finite Coxeter types but $I_2(12)$, $I_2(18)$ and $I_2(30)$, we
classify simple transitive $2$-rep\-re\-sen\-ta\-ti\-ons for the quotient of
the $2$-category of Soergel bimodules over the coinvariant algebra which is
associated to the two-sided cell that is the closest one to the two-sided cell
containing the identity element. It turns out that, in most of the cases,
simple transitive $2$-representations are exhausted by cell
$2$-representations. However, in Coxeter types $I_2(2k)$, where $k\geq 3$,
there exist simple transitive $2$-representations which are not equivalent to
cell $2$-representations.
