Dispersed domains in two-dimensional two-phase systems often exhibit complex and intriguing morphologies. For many of these systems, it is possible to predict the shape of such a domain through an evaluation of the free energy. In this paper, we extend our previous numerical technique for calculating domain shapes by allowing for titled dipoles; the original technique assumed dipole moments oriented normal to the system plane. The solution diagram is presented in the vicinity of the primary shape transition for varying tilt angles. We find that circular domains are only stable in the absence of dipole tilt. Moreover, we find that the discontinuous transition found when the dipoles are Vertical gives way to continuous elongation with increasing dipole tilt. Interestingly, it appears that the critical angle is independent of domain size.