It is shown that the weight determines the stability of the H-infinity-optimal controller for weighted sensitivity minimization problems for a large class of scalar plants and weights. Necessary and sufficient interpolation conditions on the weight are given in order for the optimal controller to be stable. An easily evaluated formula for the optimal controller is provided when the interpolation conditions are met. It is also shown that for many scalar plants it is possible to choose the weights for weighted mixed sensitivity minimization so that the optimal controller is stable and minimum-phase.