  We study limits of four-dimensional type II Calabi-Yau compactifications with
vanishing four-cycle singularities, which are dual to $\IT^2$ compactifications
of the six-dimensional non-critical string with $E_8$ symmetry. We define
proper subsectors of the full string theory, which can be consistently
decoupled. In this way we obtain rigid effective theories that have an
intrinsically stringy BPS spectrum. Geometrically the moduli spaces correspond
to special geometry of certain non-compact Calabi-Yau spaces of an intriguing
form. An equivalent description can be given in terms of Seiberg-Witten curves,
given by the elliptic simple singularities together with a peculiar choice of
meromorphic differentials. We speculate that the moduli spaces describe
non-perturbative non-critical string theories.
