In this paper, we p r o ve the integrability of the gradient ru to an exponent > 2 near the boundary, u being a weak solution of a nonlinear stationary Navier-Stokes equation under general mixed boundary conditions. As a consequence of this the pressure p belongs to the Campanato space L 2 ( ) with := n ;2 . O u r method of proof relies on an adaption of a technique by Gehring-Giaquinta-Modica (higher integrability b y reverse H older inequality) to cubes which possible intersect a h yperplane.