The parameters of a digital control design usually need to be rounded when the controller is implemented with finite precision arithmetic. This often results in degradation of the closed loop performance and reduced stability margins. This paper presents a multi-objective genetic algorithm based approach to designing the structure of a finite-precision second-order state space controller implementation, which can simultaneously minimise some set of performance degradation indices and implementation cost indices. The approach provides a set of solutions that are near Pareto-optimal, and so allows the designer to trade-off performance degradation against implementation cost. The method is illustrated by the design of the structure of a PID controller for the IFAC93 benchmark problem.