This paper will demonstrate on two advanced materials — a fibre-reinforced composite laminate (FRC) and a transformation toughened ceramic (TTC) — the importance of multicriterion optimization in the production of useful advanced materials with enhanced mechanical properties. In a previous paper (Thomsen et al., 1994a), the authors have demonstrated the application of single-criterion optimization to these materials which are based on a brittle matrix and thus prone to cracking at very low applied stresses. The optimization process aims at altering their microstructure so that all their desirable mechanical properties are enhanced. Currently, the advanced materials technologists must take a heuristic approach to meeting the often competing requirements. The present paper will show how multicriterion optimization can come to the aid of the technologists and reduce their reliance on empirical approaches.