Industry implementations of full-waveform inversion (FWI) are driven by the lower frequencies in the seismic data. This is in conflict with conventional acquisition scenarios where the free-surface ghost attenuates these desired low frequencies. In this article, we discuss the application of FWI to variable-depth streamer data and show that FWI adapts naturally to this acquisition geometry, hence benefitting from the improved low frequencies recorded in this configuration. We illustrate this with an example from the central North Sea, where detailed velocity features associated with the shallow channels in the near-surface geology are revealed by FWI. Migration with this updated velocity model improves the imaging through the near surface.