The microstructure of ferroelectric single crystals is a crucial factor that determines macroscopic properties and poling behaviour. Recent models of domain configuration, (such as that of Li & Liu, Journal of Mechanics and Physics of Solids, 2004) employ multi-rank laminate structures that satisfy compatibility in an average sense. In general, these odels result in high-rank structures, corresponding to fine microstructure. However, minimum energy structures may be expected to have low rank and to satisfy compatibility requirements at every domain wall exactly. In this paper, the criteria of exact compatibility and average compatibility are defined and then used to determine energy minimizing microstructure in the tetragonal crystal system. In addition, the lowest rank construction of compatible laminate structure for a given macroscopic state of strain and polarization is found. Based on this, poling paths from unpoled to the fullypoled state in the tetragonal system are found, which allow the structure to stay in the lowest possible rank while maintaining exact compatibility. The application of the theory to a broader class of crystal structures is discussed.