The solutions of many earthquake engineering problems involve dynamic analyses using ground-motion time series. It is often desirable to base the selection of such motions on a probabilistic estimate of the seismic hazard. The hazard density function evaluated at a chosen hazard level provides the information necessary to determine objectively the most likely earthquake events, defined by magnitude and distance, that contribute to seismic hazard. For a wide range of hazard models it is possible to show that the difference between the median motion at a site, given the occurrence of the most likely event, and the motion value corresponding to a specified hazard level, is due entirely to the modeling of random error in the strong-motion data set. This points to a straightforward approach to selecting ground-motion recordings that represent the most likely time-domain realizations of the hazard model for a given motion parameter and hazard level. Ground-motion time series selection and/or synthesis based upon this approach, for various frequency bands of the response spectrum, can provide an optimum basis for seismic design.