The IceCube Neutrino Observatory relies on an array ofphotomultiplier tubes to detect Cherenkov light produced by chargedparticles in the South Pole ice. IceCube data analyses depend on anin-depth characterization of the glacial ice, and on novelapproaches in event reconstruction that utilize fast approximationsof photoelectron yields. Here, a more accurate model is derived forevent reconstruction that better captures our current knowledge ofice optical properties. When evaluated on a Monte Carlo simulationset, the median angular resolution for in-ice particle showersimproves by over a factor of three compared to a reconstructionbased on a simplified model of the ice. The most substantialimprovement is obtained when including effects of birefringence dueto the polycrystalline structure of the ice. When evaluated on dataclassified as particle showers in the high-energy starting eventssample, a significantly improved description of the events isobserved.