We fit an ω−2 model to response spectra from eight recent Greek earthquakes ranging in size from M = 5.8 to M = 6.9. The diminution parameter κ0 was determined for each site, with a value near 0.06 for a typical soil site. The stress parameter (Δσ) showed little variation from earthquake to earthquake and had a mean value of 56 bars over all earthquakes. Predictions of peak velocity, peak acceleration, rupture duration, and fault length using the derived stress parameters are consistent with observations. Frequency-dependent site amplifications were included in all estimates; the combined effect of amplification and attenuation had a maximum value close to a factor of 2.5 for a typical soil site, relative to the motions at the surface of a perfectly elastic uniform half-space composed of materials near the source. The results form the foundation for predictions of strong motions in Greece for distances and magnitudes other than those for which data are available.