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Brownian thermal noise associated with highly reflective mirror coatings is a fundamental limit for several precision experiments, including gravitational-wave detectors. Recently, there has been a worldwide effort to find mirror coatings with improved thermal noise properties that also fulfill strict optical requirements such as low absorption and scatter. We report on the optical and mechanical properties of ion-beam-sputtered niobia and titania-niobia thin films, and we discuss application of such coatings in current and future gravitational-wave detectors. We also report an updated direct coating thermal noise measurement of the HR coatings used in Advanced LIGO and Advanced Virgo, and the observation of a discrepancy between ring-down measurements and thermal-noise estimations of mechanical loss in highly reflective mirror coatings. This discrepancy might be ascribed either to a dissipation of the silica layers considerably higher than expected or to an unexplained excess loss of stacked layers.