In order to circumvent difficulties associated with synthesising anti-windup compensators for systems containing exponentially unstable modes, we propose an alternative strategy for such systems. By elaborating on some recent results, we cast the anti-windup problem as a problem of stabilising a specially constructed outer loop, which is wrapped around the nominal system. One of the central ideas to this strategy is the transference of input constraints to output constraints, which, at least for simple systems, appears to be feasible. The success of this approach is demonstrated via a simple example.