I will analyze a model for thin film nematics whose salient feature is that one elastic constant is much larger than the others. The goal is to understand how this extreme anisotropy in elastic constants affects the morphology of singular structures emerging in the limit where the width of domain walls and the core of vortices approaches zero. This model problem sits in a regime between two well-studied energies: the BBH (Brezis/Bethuel/Helein) energy and the Aviles-Giga energy. As such, it shares features of both models, including the presence of vortex structures and walls. Our work on this problem includes an establishment of the Gamma-limit and a rigorous and computational study of minimizers of this limiting problem. This is joint work with Dmitry Golovaty (Akron) and Raghav Venkatraman (Indiana).