  A family of modified $(0,1)$ heterotic string models in D=4 is constructed in
which the strings incorporate $R$ flux tubes which may in special cases support
a local spacetime superconformal symmetry consistent with quantum mechanics.
There is an intrinsic Goldstino multiplet, so that supersymmetry breaking can
be driven by any process that generates a non-zero value for the
superpotential. The superconformal anomaly freedom of these models may be
related to a naturally vanishing $\Lambda$. The $R$ charge of such models may
also play a role in producing a generation-ordered fermion spectrum. \
