  We define the Barbasch-Evens-Magyar varieties. We show they are isomorphic to
the smooth varieties defined in [D.~Barbasch-S.~Evens '94] that map generically
finitely to symmetric orbit closures, thereby giving resolutions of
singularities in certain cases. Our definition parallels [P.~Magyar '98]'s
construction of the Bott-Samelson varieties [H.~C.~Hansen '73, M.~Demazure
'74]. From this alternative viewpoint, one deduces a graphical description in
type $A$, stratification into closed subvarieties of the same kind, and
determination of the torus-fixed points. Moreover, we explain how these
manifolds inherit a natural symplectic structure with Hamiltonian torus action.
We then express the moment polytope in terms of the moment polytope of a
Bott-Samelson variety.
