Source parameters of two shallow earthquakes have been determined by the time-domain analysis of short-period teleseismic recordings. For each event, the effect of the receiver crust was deconvolved from a set of globally distributed recordings using the homomorphic method. The resulting seismograms were compared with the form of the elastic-wave radiation computed from Savage's model of radially spreading rupture on a plane elliptical fault surface. This time-domain approach has permitted the determination of several kinematic parameters pertaining to the dynamics of rupture that are not ordinarily evaluated from spectral analysis. These parameters are rupture velocity, the direction of farthest rupture propagation, and the duration of a ramp dislocation time function which was prescribed to be the same everywhere on the fault surface. The application of a general linear inverse scheme has shown that the model parameters (notably rupture velocity and dimension) are only weakly coupled. Inversion is also used to determine the range of acceptable parameter values and indicates the importance of array recordings in constraining the models. A consistent discrepancy between the observed and model seismograms during the first half-cycle of motion is attributed to the incorrect prescription of the dislocation time function. It is suggested that a space-dependent function determined theoretically by Kostrov in 1964 would tend to remove this discrepancy.