Abstract: Self-checking design based on unordered codes requires that the target circuit is transformed into an unidirectional circuit. Techniques for the design of unidirectional circuits have been proposed. However, in general, multilevel logic optimization techniques cannot be directly applied because they do not guaranty the unidirectional property is preserved. In this paper we will show how structural logic optimization methods can be successfully constrained for the optimization of unidirectional circuits. Experimental results show that the area overhead produced by making a circuit unidirectional can be largely reduced and the circuits can be optimized to a smaller area than the original non-unidirectional benchmarks on average.