Earthquake‐radiated motions contain information that can be interpreted as source displacement and therefore related to stress drop. Except in a few notable cases, these displacements cannot be easily related to the absolute stress level or the fault strength, or attributed to a particular physical mechanism. In contrast, paleoearthquakes recorded by exhumed pseudotachylite have a known dynamic mechanism whose properties constrain the coseismic fault strength. Pseudotachylite can be used to directly address a discrepancy between seismologically measured stress drops, which are typically a few MPa, and much larger dynamic stress drops expected from thermal weakening during slip at seismic speeds in crystalline rock (Mckenzie and Brune, 1972; Sibson, 1973; Lachenbruch, 1980; Mase and Smith, 1987; Rice, 2006), and as have been observed in laboratory experiments at high slip rates (Di Toro, Hirose, Nielsen, Pennacchioni, et al., 2006). This places pseudotachylite‐derived estimates of fault strength and inferred crustal stress within the context and bounds of naturally observed earthquake source parameters: apparent stress, stress drop, and overshoot, including consideration of fault‐surface roughness, off‐fault damage, fracture energy, and the strength excess. The analysis, which assumes stress drop is related to corner frequency as in the Madariaga (1976) source model, is restricted to earthquakes of the Gole Larghe fault zone in the Italian Alps, where the dynamic shear strength is well constrained by field and laboratory measurements. We find that radiated energy is similar to or exceeds the shear‐generated heat and that the maximum strength excess is ∼16 MPa. These events have inferred earthquake source parameters that are rare, for instance, a low percentage of the global earthquake population has stress drops as large, unless fracture energy is routinely greater than in existing models, pseudotachylite is not representative of the shear strength during the earthquake that generated it, or the strength excess is larger than we have allowed.