The problem treated concerns the design of a single controller which simultaneously stabilises two nonconcentric balls of single-input/single-output plants. This is done by using the normalised left coprime factor plant description with H(infinity)-bounded uncertainty to characterise each plant ball. Necessary conditions for being able to solve this problem are developed and used to provide a computational approach for determining a controller. Several examples are given to demonstrate the validity of the necessary conditions and the controller synthesis procedure.