It is shown how one can choose suitable combinations of Siberian Snakes and betatron phase advances to optimize the ability of a ring to accelerate a polarized beam with little reduction of polarization. In an analysis of HERA‐p, these methods have lead to a 14‐fold increase of the vertical beam emittance for which polarization could be preserved. This is not only impressive as a result, but also the methods which lead to this result are very interesting. They contain detailed spin‐orbit tracking and the application of the Froissart‐Stora Formula for higher order spin‐orbit resonances, for which an algorithm of determining resonance strength has been found. © 2003 American Institute of Physics