  We determine for which Coxeter types the associated small quotient of the
$2$-category of Soergel bimodules is finitary and, for such a small quotient,
classify the simple transitive $2$-representations (sometimes under the
additional assumption of gradability). We also describe the underlying
categories of the simple transitive $2$-representations. For the small
quotients of general Coxeter types, we give a description for the cell
$2$-representations.
