Proper evaluation of seismic hazard depends on accurate estimates of potential earthquake size. In areas with complex, multisegment fault systems, such an estimate in turn depends on an ability to predict the circumstances under which rupture may jump between fault segments. Many observational and numerical studies have analyzed the phenomenon of jumping rupture, but none has focused on how the process of rupture termination on the primary (nucleating) fault segment affects the ability of rupture to jump to a secondary fault segment. In the current study, I model the dynamics of a simple 2D strike-slip fault system with two parallel segments arranged with either a compressional or extensional stepover. I vary the suddenness with which the initial shear stress tapers to zero on the primary section. If the initial shear stress goes to zero over a very small (100 m) distance, rupture readily jumps both compressional and extensional stepovers of 1 km. If the initial shear stress tapers to zero over 1 km, rupture can jump the compressional stepover, but not the extensional stepover. If the initial shear stress tapers to zero over 2.5 km, rupture cannot jump either the compressional or the extensional stepover. The results illustrate the importance of the slip gradient (and the resultant static stress field) and the acceleration of the rupture front (and the resultant generation of stopping phases) in determining the probability of jumping rupture.