Piezoelectric ceramics contain anomalies which give rise to localized stress concentrations when electric fields are applied. These stress concentrations cause microcracking which leads to electro-mechanical degradation and eventually to material failure. In this paper, a unit cell approach is presented to understand the relationship between material properties and electric field induced stress concentrations around a specific anomaly, i.e., circular void. An exact electro-elastic analysis verified with a finite element model is used to study the stress and electric field concentrations as a function of material properties. Parametric studies indicate that the electric field induced stress concentrations in the material are effectively eliminated for certain values of the piezoelectric coefficients. While a trivial solution to this problem is that the piezoelectric coefficients are zero, other "optimum" coefficients exist. These coefficients do not limit the deformation profile of the piezoelectric and are thermodynamically admissible. Results presented for PZT-4 and PZT-5H support the contention that optimal piezoelectric materials can be manufactured.