The traditional approach to the search for improved materials, such as thermoelectric materials, involves the sequential synthesis and characterization of new compounds, followed by the investigation of their properties. Each single solid state compound has materials interaction parameters (e.g., degree of orbital overlap, orbital energy, band energies etc.) that determine its thermoelectric properties. These interaction parameters can be used to define a phase space, in which individual compounds are represented by a single point. Because this phase space can be rapidly explored with pressure, our efforts have focused on the synthesis of complex semiconductors and rare earth based materials, followed by pressure-tuning studies of their thermoelectric properties. This approach to exploring interaction parameter phase space potentially allows the thermoelectric power to be more rapidly and cleanly optimized than is possible with the traditional approach. Here we present some results for rare earth thermoelectric compounds that have been pressure-tuned. Demonstration of the existence of materials with improved ZT at high pressure can also provide insight into the structural and electronic parameters necessary to achieve high figures of merit at ambient pressure.