Ion mobility spectrometry (IMS) is increasingly employed to probe the structures of gas-phase ions, particularly those of proteins and other biological macromolecules. This process involves comparing measured mobilities to those computed for potential geometries, which requires evaluation of orientationally averaged cross sections using some approximate treatment of ion-buffer gas collisions. Two common models are the projection approximation (PA) and exact hard-spheres scattering (EHSS) that represent ions as collections of hard spheres. Though calculations for large ions and/or conformer ensembles take significant time, no algorithmic optimization had been explored. Previous EHSS programs were dominated by ion rotation operations that allow orientational averaging. We have developed two new algorithms for PA and EHSS calculations: one simplifies those operations and greatly reduces their number, and the other disposes of them altogether by propagating trajectories from a random origin. The new algorithms were tested for a representative set of seven ion geometries including diverse sizes and shapes. While the best choice depends on the geometry in a nonobvious way, the difference between the two codes is generally modest. Both are much more efficient than the existing software, for example faster than the widely used Mobcal (implementing EHSS) similar to 10-30-fold.