  In arXiv:1407.7580 a mechanism to fix the closed string moduli in a de Sitter
minimum was proposed: a D-term potential generates a linear relation between
the volumes of two rigid divisors which in turn produces at lower energies a
race-track potential with de Sitter minima at exponentially large volume. In
this paper, we systematically search for implementations of this mechanism
among all toric Calabi-Yau hypersurfaces with $h^{1,1}\leq 4$ from the
Kreuzer-Skarke list. For these, topological data can be computed explicitly
allowing us to find the subset of three-folds which have two rigid toric
divisors that do not intersect each other and that are orthogonal to
$h^{1,1}-2$ independent four-cycles. These manifolds allow to find D7-brane
configurations compatible with the de Sitter uplift mechanism and we find an
abundance of consistent choices of D7-brane fluxes inducing D-terms leading to
a de Sitter minimum. Finally, we work out a couple of models in detail,
checking the global consistency conditions and computing the value of the
potential at the minimum.
