The definition of the scattering volume for p-wave collisions needs to be generalized in the presence of dipolar interactions for which the potential decreases with the interparticle separation as 1/R 3 . Here, we propose a generalized definition of the scattering volume characterizing the short-range interactions in odd-parity waves, obtained from an analysis of the p-wave component of the twobody threshold wave function. Our approach uses an asymptotic model and introduces explicitly the anisotropic dipole-dipole interaction, which governs the ultracold collision dynamics at long-range. The short-range interactions, which are essential to describe threshold resonances, are taken into account by a single parameter which is determined by the field-free s-wave scattering length. arXiv:1807.05783v2 [quant-ph]