A procedure is presented to design and optimize the contour of a hypersonic wind tunnel nozzle with a goal of minimizing exit flow nonuniformity. The procedure uses a Navier-stokes solver that admits chemical and vibrational nonequilibrium thermodynamics and high-pressure effects. The two-step optimization process is accomplished with a basic least-squares optimization (LSO) method. The first step of the design procedure begins with an existing inviscid irrotational method of characteristics (MOC) that is limited to thermally and calorically perfect gas (TCPG). MOC is used to design an inviscid contour, which is then corrected with a boundary layer displacement thickness from an integral momentum formulation. The deleterious effects of the TCPG assumption are ameliorated by using an effective specific-heat ratio an effective gas constant the TCPG computation yields the same exit Mach number and velocity as a quasi-one-dimensional computation based on thermochemical equilibrium. The MOC based contour is then formally optimized using the LSO method, treating various MOC program input variables as formal design parameters. The objective function is the square deviation of flow properties from target values at the nozzle exit, excluding the boundary layer, and is computed with the Navier-Stokes solver. The flow properties chosen for the objective function are the velocity components and the static pressure and density. After the MOC contour is optimized, the second step of the optimization procedure commences. In the second step, the contour is further perturbed by adding a small correction distribution represented as a cubic spline fitted to a limited number of nodes along the contour. The correction values of the nozzle radius are the formal design parameters for the next application of LSO.