  We study moduli stabilization via fluxes in the $2^6$ Landau-Ginzburg model.
Fluxes not only give masses to scalar fields but can also induce higher order
couplings that stabilize massless fields. We investigate this for several
different flux choices in the $2^6$ model and find two examples that are
inconsistent with the Refined Tadpole Conjecture. We also present, to our
knowledge, the first 4d $\mathcal{N}=1$ Minkowski solution in string theory
without any flat direction.
