The cross-machine-direction (CD) control problem in paper machines is analysed from the viewpoint of robust performance. The objective of robust performance is to maintain control system stability and to satisfy a bound on the maximum singular value of the closed-loop sensitivity function despite modelling error. Characteristics common to all CD response control problems including paper basis-weight control are identified. The response of an important actuator for basis-weight control, the paper machine slice, is described by a single dimensionless design parameter that provides considerable insight about the CD response control problem. Sufficient conditions allowing design of robust diagonal controllers are developed. Robust stability, performance and failure tolerance properties of the controllers are proven.