The IceCube Neutrino Observatory instruments about 1 km$^3$ of deep, glacial ice at the geographic South Pole using 5160 photomultipliers to detect Cherenkov light of charged relativistic particles. Most of IceCube's science goals rely heavily on an ever more precise understanding of the optical properties of the instrumented ice. A curious light propagation effect observed by the experiment is an anisotropic attenuation, which is aligned with the local flow of the ice. Having recently identified curved photon trajectories resulting from asymmetric light diffusion in the birefringent polycrystalline microstructure of the ice as the most likely underlying cause of this effect, work is now ongoing to optimize the model parameters (effectively deducing the average crystal size and shape in the detector). We present the parametrization of the birefringence effect in our photon propagation simulation, the fitting procedures and results as well as the impact of the new ice model on data-MC agreement.