An arrangement and method for radially positioning a brush seal relative to a rotor provides a main seal segment having a slot open toward the rotor and an interior ledge facing away from the rotor, a brush seal segment in the slot and having an exterior shoulder facing toward the rotor and overlying the interior ledge such that the brush seal segment can move radially relative to the main seal segment and rotor and the exterior shoulder can move toward and away from the interior ledge, a shim disposed and establishing a minimum spacing between the interior ledge and the exterior shoulder, and set screws tightened into spaced threaded holes in the main seal segment forcing the exterior shoulder against the shim and to the minimum spacing from the interior ledge so as to prevent radial floating of the brush seal segment in the slot.