  We present first steps toward understanding the ultracold scattering
properties of polar molecules in strong electric field-seeking states. We have
found that the elastic cross section displays a quasi-regular set of potential
resonances as a function of the electric field, which potentially offers
intimate details about the inter-molecular interaction. We illustrate these
resonances in a ``toy'' model composed of pure dipoles, and in more physically
realistic systems. To analyze these resonances, we use a simple WKB
approximation to the eigenphase, which proves both reasonably accurate and
meaningful. A general treatment of the Stark effect and dipolar interactions is
also presented.
