Full-waveform inversion (FWI) aims to resolve an ill-posed non-linear optimization problem in order to retrieve unknown subsurface model parameters with high resolution from seismic data. The non-linearity, in the absence of low frequencies from the recorded seismic signal, tends to increase, especially for large-velocity structures, like salt bodies and the sediments beneath them, and often prevents the inversion from obtaining an adequate model. To alleviate the ill-posedness of FWI for salt-bodies, we propose to utilize model regularization in order to promote a limited variation in the inverted model and a salt-flooding regularization from the top of the salt (without picking). On that account, we split the optimization problem into two parts: first, we minimize the data misfit and the total variation in the model, seeking to achieve an inverted model with sharp interfaces; and second, we penalize sharp velocity drops in the model by a computational flooding of the velocity field. Unlike conventional industrial salt flooding, our proposed technique requires minimal human intervention and no information whatsoever about the top of the salt. Those features are demonstrated on a dataset of the Sigsbee2A model in which the lowest available frequency is 3 Hz. We retrieve most of the salt region and also some of the fine sedimentary layering beneath the salt.