To overcome the local minima problem in FWI, we propose to use an auxiliary data-domain objective function during inversion. It reduces the data to a simpler form by squaring, followed by blurring to ensure that events that are too far apart can still interact during the inversion. As it effectively replaces seismic arrivals by bumps, we call it the bump functional. This objective function is less sensitive to cycle skipping. Its role is to guide the inversion towards the global minimum by pulling the trapped solution out of the local minima associated with the least-squares functional whenever necessary. Waveform inversion cannot be performed with only the auxiliary objective function because it is insensitive to the polarity of the arrivals and the source signature. Therefore, we alternate between minimization with this and the classic least-squares functional. We confirm the validity of the approach using a simple numerical example with reflection data.