Underwater images are altered by the physical characteristics of the medium through which light rays pass before reaching the optical sensor. Scattering and strong wavelength-dependent absorption significantly modify the captured colors depending on the distance of observed elements to the image plane. In this paper, we aim to recover the original colors of the scene as if the water had no effect on them. We propose two novel methods that rely on different sets of inputs. The first assumes that pixel intensities in the restored image are normally distributed within each color channel, leading to an alternative optimization of the well-known \textit{Sea-thru} method which acts on single images and their distance maps. We additionally introduce SUCRe, a new method that further exploits the scene's 3D Structure for Underwater Color Restoration. By following points in multiple images and tracking their intensities at different distances to the sensor we constrain the optimization of the image formation model parameters. When compared to similar existing approaches, SUCRe provides clear improvements in a variety of scenarios ranging from natural light to deep-sea environments. The code for both approaches is publicly available at https://github.com/clementinboittiaux/sucre .