Rapid sea level rise due to an ice sheet collapse has the potential to be extremely damaging the coastal communities and infrastructure. Blocking deep warm water with thin flexible buoyant underwater curtains may reduce melting of buttressing ice shelves and thereby slow the rate of sea level rise. Here, we use new multibeam bathymetric datasets, combined with a cost-benefit model, to evaluate potential curtain routes in the Amundsen Sea. We organize potential curtain routes along a "difficulty ladder"representing an implementation pathway that might be followed as technological capabilities improve. The first curtain blocks a single narrow (5 km) submarine choke point that represents the primary warm water inflow route towards western Thwaites Glacier, the most vulnerable part of the most vulnerable glacier in Antarctica. Later curtains cross larger and deeper swaths of seabed, thus increasing their cost, while also protecting more of the ice sheet, increasing their benefit. In our simple cost-benefit analysis, all of the curtain routes achieve their peak value at target blocking depths between 500 and 550 m. The favorable cost-benefit ratios of these curtain routes, along with the trans-generational and societal equity of preserving the ice sheets near their present state, argue for increased research into buoyant curtains as a means of ice sheet preservation, including high-resolution fluid-structural and oceanographic modeling of deep water flow over and through the curtains, and coupled ice-ocean modeling of the dynamic response of the ice sheet.