So long as there is some finite specific fracture energy involved in earthquake rupture, the rupture velocity cannot exceed the Rayleigh-wave velocity in the direction of mode II extension, or the S-wave velocity in the direction of mode III extension. The radiation efficiency, which is the fraction of available energy that goes into seismic waves, depends upon the rupture velocity. It is zero if the crack grows quasi- statically, increases with rupture velocity, and tends to unity as the velocity approaches the limiting value appropriate to the mode of extension. A model involving a semi-infinite crack in antiplane shear (mode III) which accelerates rapidly to a velocity and runs at this velocity until it is arrested by a barrier of higher fracture energy, yields a formula for estimating the specific fracture energy. This formula provides a reasonable estimate of the specific fracture energy involved in an earthquake that is insensitive to the mode of arrest of the rupture.