We determined the stress parameter, Δσ, for the eight earthquakes studied by Atkinson and Boore (2006), using an updated dataset and a revised point-source stochastic model that captures the effect of a finite fault. We consider four geometrical-spreading functions, ranging from 1/R at all distances to two- or three-part functions. The Δσ values are sensitive to the rate of geometrical spreading at close distances, with 1/R1.3 spreading implying much higher Δσ than models with 1/R spreading. The important difference in ground motions of most engineering concern, however, arises not from whether the geometrical spreading is 1/R1.3 or 1/R at close distances, but from whether a region of flat or increasing geometrical spreading at intermediate distances is present, as long as Δσ is constrained by data that are largely at distances of 100 km–800 km. The simple 1/R model fits the sparse data for the eight events as well as do more complex models determined from larger datasets (where the larger datasets were used in our previous ground-motion prediction equations); this suggests that uncertainty in attenuation rates is an important component of epistemic uncertainty in ground-motion modeling. For the attenuation model used by Atkinson and Boore (2006), the average value of Δσ from the point-source model ranges from 180 bars to 250 bars, depending on whether or not the stress parameter from the 1988 Saguenay earthquake is included in the average. We also find that Δσ for a given earthquake is sensitive to its moment magnitude M, with a change of 0.1 magnitude units producing a factor of 1.3 change in the derived Δσ.