  A random matrix model definition of a family of ${\cal N}{=}1$ supersymmetric
extensions of the Virasoro minimal string of Collier, Eberhardt, M\"{u}hlmann,
and Rodriguez is presented. An analysis of the defining string equations shows
that the models all naturally have unambiguous non-perturbative completions,
which are explicitly supplied by the double-scaled orthogonal polynomial
techniques employed. Perturbatively, the multi-loop correlation functions of
the model define a special supersymmetric class of "quantum volumes",
generalizing the prototype case. For two of the models the volumes vanish to
all orders in the perturbative topological expansion. This amounts to a
prediction for expected related computations in 3D gravity and 2D dilaton
gravity.
