The classical optimization of two-dimensional supersonic inlets for maximum total pressure recovery is extended to two-dimensional scramjet inlets. The result that optimal supersonic inlets have shock waves of equal strength is often applied to scramjets, However the typical flow turning constraint required for scramjets, along with the lack of a terminating normal shock, lead to a more involved optimization problem. Despite this, optimization by the method of Lagrange multipliers indicates that scramjet inlets with maximum total pressure recovery have external shocks with almost equal strength. The optimal total pressure recovery and turning angles for some typical scramjet inlet configurations with up to five shocks are presented.