Computer simulation of ion motion in a quadrupole mass spectrometer has been used to examine the effect of initial ion conditions on performance when operated in the first and third zones of the Mathieu stability diagram. Commercial instruments frequently use round electrodes instead of the better-performing hyperbolic electrodes because the cost of manufacturing is lower. However, adverse features are seen when using round electrodes. Here further insight is provided and a possible method of correction is suggested. For the first time, ion origin for the first stability region for a round electrode quadrupole has been reported. © 2005 American Vacuum Society.