The problem of output constraints in linear systems is considered, and a new methodology which helps the closed loop respect these limits is described. The new methodology invokes ideas from the antiwindup literature in order to address the problem from a practical point of view. This leads to a design procedure very much like that found in antiwindup design. First, a linear controller ignoring output constraints is designed. Then, an additional compensation network which ensures that the output limits are, as far as possible, respected is added. As the constraints occur at the output, global results can be obtained for both stable and unstable plants.