Compositions in the ZrO2-Y2O3-Ta2O5 system are of interest as low thermal conductivity, fracture resistant oxides for the next generation thermal barrier coatings (TBC). Multiple phases occur in the system offering the opportunity to compare the thermal properties of single, two-phase, and three-phase materials. Despite rather large variations in compositions almost all the solid solution compounds had rather similar thermal conductivities and, furthermore, exhibited only relatively small variations with temperature up to 1000 o C. These characteristics are attributed to the extensive mass disorder in all the compounds and, in turn, small interfacial Kapitza (thermal) resistances. More complicated behavior, associated with the transformation from the tetragonal to monoclinic phase, occurs on long-term annealing in air of some of the compositions. However, the phases in two of the compositional regions do not change with annealing in air and their thermal conductivities remain unchanged suggesting they may be suitable for further exploration as thermally stable TBC overcoats.