We model a procedural reform aimed at restoring a proper role for the minority in the confirmation process of judicial nominations in the US Senate. We propose that nominations to the same level court be collected in periodic lists and voted upon individually with storable votes, allowing each senator to allocate freely across the list a fixed number of total votes. Although each nomination is decided by simple majority, storable votes make it possible for the minority to win occasionally, but only when the relative importance its members assign to a nomination is higher than the relative importance assigned by the majority. Numerical simulations approximate the composition of the 113th and 114th Senates. Under plausible assumptions motivated by a game theoretic model, we find that a minority of 45 senators would be able to win about 20 percent of confirmation battles when the majority party controls the presidency, and between 40 and 60 percent when the president identifies with the minority party. For most parameter values, the possibility of minority victories increases aggregate welfare.