Controlling the complex nanostructures that often form in cation-deficient oxides may provide an effective way to tailor their thermophysical properties, but this remains a challenging task. We report a study of un-doped and Hf-doped YTa3O9 with a Y-deficient double-perovskite structure using high-temperature X-ray diffraction, electron diffraction, and small-angle X-ray scattering. Undoped YTa3O9 has an orthorhombic structure with 90° and 180° domain walls and stacking faults observed at the micro and nano levels at room temperature. It undergoes a phase transition to a tetragonal phase, with an associated volume change, at around 700 K. Doping of the materials with Hf successfully stabilizes a tetragonal phase that includes a superstructure with periodic distances of a few nanometers at room temperature. The thermal conductivity of Hf-doped YTa3O9 is lower than that of the undoped material, suggesting that the interfaces between nanodomains interfere with diffusive thermal transport.