This paper presents a parameter space approach to constrained variance and minimum variance PID controller design for LTI models. The technique is based on rational transfer functions of the plant and noise models. Loci corresponding to a fixed variance can be mapped into parameter planes for PID and PI type controllers to graphically display regions which satisfy the constraint, thereby guiding a design to appropriate controller gains. Requirements for tracking regulation can be readily achieved without excessively increasing the output variance. The usual advantages of parameter space techniques apply where other design criteria may be superimposed, allowing multiple objectives to be achieved non-conservatively. The superposition of the parameter space boundaries from existing robust control techniques thus allows non-conservative robust minimum variance PID design. A design example compares the technique to an algebraic minimum variance design using an integrator when tracking is required. (C) 2008 Elsevier Ltd. All rights reserved.