We have taken advantage of the recent increase in strong-motion data at close distances to derive new attenuation relations for peak horizontal acceleration and velocity. Acceleration data from 183 recordings of 24 earthquakes and velocity data from 62 recordings of 10 earthquakes have been used. This new analysis uses a magnitude-independent shape for the attenuation curve based on geometrical spreading and anelastic attenuation. A magnitude-dependent shape could be accommodated by the method, but the data do not support it. An innovation in technique is introduced that decouples the determination of the distance dependence of the data from the magnitude dependence.