Investigations of the local structure about defect atoms in several lightly doped materials with the emphasis on the continued study of off-center systems and the conditions for off- center behavior. The paraelectric-paraelastic tunneling centers represent ideal test systems for understanding low temperature tunneling behavior. Paraelectric resonance, dielectric constant measurements, and Extended X-ray Absorption Fine Structure (EXAFS) studies will be made on systems such as KCL with substitutional Li ions, NaBr with substitutional F ions, and KI with substitutional Ag ions as a function of hydrostatic pressure. Pressure moves the off-center defects back on center and leads to information relating to the conditions for the off- center displacement. It is also hoped to study off-center defects at much higher concentrations above the solubility limits as a function of temperature. It is hoped this work will have some connection to tunneling behavior in glasses.