An exemplary gas turbine engine component assembly includes, among other things, a case having a generally cylindrical outer surface. At least one synchronizing ring is received at least partially about the outer surface of the case. A plurality shims situated between an inner surface on the at least one synchronizing ring and the outer surface of the case at a plurality of shim locations are circumferentially spaced about the case outer surface. Each shim location includes at least one of the shims. A radial thickness of the shims at a first one of the shim locations is different than the radial thickness of the shims at a second one of the shim locations.