  We explore the T-duality web of 6D Heterotic Little String Theories, focusing
on flavor algebra reducing deformations. A careful analysis of the full flavor
algebra, including Abelian factors, shows that the flavor rank is preserved
under T-duality. This suggests a new T-duality invariant in addition to the
Coulomb branch dimension and the two-group structure constants. We also
engineer Little String Theories with non-simply laced flavor algebras, whose
appearance we attribute to certain discrete 3-form fluxes in M-theory.
Geometrically, these theories are engineered in F-theory with non-K\"ahler
favorable K3 fibers. This geometric origin leads us to propose that freezing
fluxes are preserved across T-duality. Along the way, we discuss various exotic
models, including two inequivalent $\text{Spin(32)}/\mathbb{Z}_2$ models that
are dual to the same $\text{E}_8 \times \text{E}_8$ theory, and a family of
self-T-dual models.
