Reliable ground-motion prediction for future earthquakes depends on the ability to simulate realistic earthquake source models. Though dynamic rupture calculations have recently become more popular, they are still computationally demanding. An alternative is to invoke the framework of pseudodynamic (PD) source characterizations that use simple relationships between kinematic and dynamic source parameters to build physically self-consistent kinematic models. Based on the PD approach of Guatteri et al. (2004), we propose new relationships for PD models for moderate-to-large strike-slip earthquakes that include local supershear rupture speed due to stress heterogeneities. We conduct dynamic rupture simulations using stochastic initial stress distributions to generate a suite of source models in the magnitude Mw 6–8. This set of models shows that local supershear rupture speed prevails for all earthquake sizes, and that the local rise-time distribution is not controlled by the overall fault geometry, but rather by local stress changes on the faults. Based on these findings, we derive a new set of relations for the proposed PD source characterization that accounts for earthquake size, buried and surface ruptures, and includes local rise-time variations and supershear rupture speed. By applying the proposed PD source characterization to several well-recorded past earthquakes, we verify that significant improvements in fitting synthetic ground motion to observed ones is achieved when comparing our new approach with the model of Guatteri et al. (2004). The proposed PD methodology can be implemented into ground-motion simulation tools for more physically reliable prediction of shaking in future earthquakes.