Carbon dioxide is sequestered in a formation using a dual completion and injection method that reduces or eliminates upward leak rates of the sequestered carbon dioxide. The dual completion and injection method involves the injection of a benign fluid such as brine (water) into a permeable layer of the formation located above the sequestration layer and which is separated form the sequestration layer by a nearly impermeable layer. The water is preferably injected at the same time the carbon dioxide is injected.