Recall {that a} module M over some ring R is pseudo-coherent if it admits a decision whose phrases are finitely generated projective R-modules. Such a module is reflexive when considered an object within the derived class $D(Mod_R)$, i.e.,
$$M to RHom(RHom(M, R), R))$$
is a quasi-isomorphism, the place RHom denotes the derived functor of the standard homomorphisms of R-modules.

Does the converse maintain? (Possibly for good rings?), i.e., are reflexive modules (the place reflexivity is at all times understood within the derived sense) pseudo-coherent?