A new tuning method for robust decentralised PI controllers is given. The controller tunings are obtained by minimising a robust performance criterion. The cost function to be minimised is derived from the standard mu-synthesis criterion and it takes into account the process uncertainty and the desired performance. A constraint on the variations of the controller outputs can also be added to the performance criterion. The two options, with and without a constraint, respect the specifications in a minimal way to limit the controller output variations obtained from the standard mu-synthesis criterion. These two options and the standard mu-synthesis criterion are compared on an ill-conditioned two-input two-output (TITO) process example. The generalised step response for TITO processes is used to analyse the time behaviour of closed-loop systems.