  We define a family of string equations with perturbative expansions that
admit an interpretation as an unoriented minimal string theory with background
D-branes and R-R fluxes. The theory also has a well-defined non-perturbative
sector and we expect it to have a continuum interpretation as an orientifold
projection of the non-critical type~0A string for \hat{c}=0, the (2,4) model.
There is a second perturbative region which is consistent with an
interpretation in terms of background R-R fluxes. We identify a natural
parameter in the formulation that we speculate may have an interpretation as
characterizing the contribution of a new type of background D-brane. There is a
non-perturbative map to a family of string equations which we expect to be the
\hat{c}=0 type 0B string. The map exchanges D-branes and R-R fluxes. We present
the general structure of the string equations for the (2,4k) type 0A models.
