Worldwide tank spills represent 10% of the average annual input of oil in the sea. When such spills arise from wrecks at depth, neutralisation of environmental impacts is difficult to achieve. Extracting oil from sunken tankers is expensive, and, unfortunately, all of the oil cannot be extracted, as the Prestige case demonstrates. We propose an environmentally appropriate, cost-effective and proactive method to stop the long-term problem of leaks from sunken tankers similar to the Prestige. This method confines the wreck with a "sediment" capping of sepiolite mineral that emulates a natural sediment. A set of experiments and simulations shows that sepiolite has the characteristics necessary to accomplish the confinement of any current or future sunken tanker with minimal environmental perturbation.