  We discuss deformations of orbifold singularities on tilted tori in the
context of Type IIA orientifold model building with D6-branes on special
Lagrangian cycles. Starting from $T^6/(\mathbb{Z}_2 \times \mathbb{Z}_2)$, we
mod out an additional $\mathbb{Z}_3$ symmetry to describe phenomenologically
appealing backgrounds and reduce to $\mathbb{Z}_3$ and $\Omega\mathcal{R}$
invariant orbits of deformations. While D6-branes carrying SO(2N) or USp(2N)
gauge groups do not constrain deformations, D6-branes with U(N) gauge groups
develop non-vanishing D-terms if they couple to previously singular, now
deformed cycles. We present examples for both types of D6-branes, and in a
three-generation Pati-Salam model on $T^6/(\mathbb{Z}_2 \times \mathbb{Z}_6')$
we find that ten out of 15 twisted complex structure moduli are indeed
stabilised at the orbifold point by the existence of the brane stacks.
