Many seismic imaging techniques require computing traveltimes and travel paths. Methods to compute raypaths are usually based on high-frequency approximations. In situations such as head waves, these raypaths minimize traveltime but are not paths along which most of the energy travels. We have developed a new approach to computing raypaths, using a modification of ray bending that we call wave tracing; it computes raypaths and traveltimes that are more consistent with the paths and times for the band-limited signals in real data than the paths and times obtained using high-frequency approximations. Wave tracing shortens the raypath while keeping the raypath within the Fresnel zone for a characteristic frequency of the signal.