  Gravity duals for little string theories --- which give rise to
four-dimensional theories that undergo permanent confinement in the infrared
--- have not been studied in great detail. We address this question in the
framework of heterotic SO(32) and E_8 x E_8 string theory, constructing these
backgrounds by wrapping heterotic five-branes on calibrated two-cycles of
non-Kahler resolved conifolds. Related to deformations of the underlying little
string theories, we find numerous analytic solutions preserving N = 1
supersymmetry in four-dimensions. These theories all have non-abelian global
symmetries that generally arise from both the heterotic vector bundle and from
certain orbifold states. In the decoupling limit, we argue that the gravity
duals are given by non-Kahler manifolds that have both blown-up two-cycles and
three-cycles at the origin. We argue this following certain duality sequences
that include M-theory torsional manifolds at an intermediate step, which help
us to construct new type I' gauge/gravity duality pairs. In the M-theory
duality frame, we also elucidate new sequences of flips and flops.
