New high-signal/noise 13CO observations of the bipolar outflow in the molecular cloud L1551 are reported. Contrary to earlier observations of CO J = 1-0 and 2-1, no strong spatial dependence is found for the velocity profile of these spectra. The implications of these observations are such that the model of an empty shell for this source is less likely, and a model consisting of a shell which contains significant amounts of outflowing molecular gas inside the swept-up cavity walls is suggested
