We use the spectral-element method to simulate ground motion generated by two recent and well-recorded small earthquakes in the Los Angeles basin. Simulations are performed using a new sedimentary basin model that is constrained by hundreds of petroleum-industry well logs and more than 20,000 km of seismic reflection profiles. The numerical simulations account for 3D variations of seismic-wave speeds and density, topography and bathymetry, and attenuation. Simulations for the 9 September 2001 Mw 4.2 Hollywood earthquake and the 3 September 2002 Mw 4.2 Yorba Linda earthquake demonstrate that the combination of a detailed sedimentary basin model and an accurate numerical technique facilitates the simulation of ground motion at periods of 2 sec and longer inside the basin model and 6 sec and longer in the regional model. Peak ground displacement, velocity, and acceleration maps illustrate that significant amplification occurs in the basin.