Simulations using coupled ice-ocean models forced with the atmospheric output of the HadCM3 SRES-A1B scenario run show that the circulation in the southern Weddell Sea changes during the 21st century. Derivatives of Circumpolar Deep Water are directed southward underneath the Filchner-Ronne Ice Shelf, warming the cavity and drastically increasing basal melting. To find out whether the open ocean always will supply the 'fuel' for melting, we continue our simulations, applying 20th-century atmospheric forcing alone or together with prescribed basal mass flux at the end of (or during) the SRES-A1B scenario run. The results identify a tipping point in the southern Weddell Sea: Once warm water flushes the ice shelf cavity a positive melt water feedback enhances the shelf circulation and the onshore transport of open ocean heat. The process cannot be stopped solely by returning to 20th-century atmospheric forcing and needs a significant reduction to 20th-century basal melt rates. This finding has implications for the future Antarctic Ice Sheet, because the prescribed small melt water input can only be achieved in reality by a significant loss of its floating portions.