In the rhyolite system Qz-Ab-Or-(An-H2O) the position of the cotectic curve separating the quartz and feldspar(s) stability fields depends on pressure, making it a potential geobarometer applicable to high SiO2 volcanic products if the melt H2O contents are known. Until the recent years, the applicability of this geobarometer has been very limited, as the pressure effect can be largely obscured by the near ubiquitous presence of normative anorthite (An, CaSi2Al2O8) in the melt. In this study new phase diagrams are presented that make it possible to constrain the position of eutectic points and cotectic curves at various pressures and melt normative An contents. Data were derived experimentally by conducting crystallization experiments to determine phase diagrams at following conditions: 200 MPa, 1.4 wt.% H2O, 3.5 wt.% An; 200 MPa, 1.3 wt.% H2O, 7 wt.% An; 500 MPa, 3 wt.% H2O, 3.5 wt.% An; 500 MPa, 1.4 wt.% H2O, 3.5 wt.% An and 500 MPa, 1.3 wt.% H2O, 7 wt.% An. Using this database and previous results on phase equilibria, a geobarometer is constructed based on the effect of the main parameters influencing the cotectic compositions in the rhyolitic system: pressure, melt water content and melt An content. This new geobarometer DERP (Determining Eutectic Rhyolite Pressures) is calibrated to calculate pressures of magma storage from the compositions of cotectic glasses with up to 7 wt.% normative melt An. DERP is calibrated for any melt H2O content in the pressure range 50 – 500 MPa and its application is restricted to high silica rhyolitic systems saturated with respect to quartz and feldspar(s). DERP was tested successfully against various independent methods of pressure estimation in rhyolites available in the literature (with r² > 80% and an overall error of less than 100 MPa). The comparison of pressures estimated with DERP and rhyolite-MELTS, which are two barometers based on the same approach, indicates that rhyolite-MELTS, calibrated using an old dataset, underestimates the effect of An. With DERP now available, pressure estimates can be made for the relatively dry rhyolites of the Snake River Plain, Yellowstone (SRPY), USA, where this was hardly possible before. The SRPY was formed by the movement of the northamerican Plate over a fix mantle plume. This process created over the course of the last ~ 17 Ma several eruptive complexes and caused numerous volcanic eruptions with huge volumes of rhyolitic material deposited in the area. The eruptive centers are McDermit (McD, 16.5 Ma), Owyhee-Humboldt (OH, 15.3 Ma), Bruneau-Jarbidge (BJ, 12.7 Ma), Twin Falls (TF, 10.5 Ma), Picabo (P, 10.2 Ma), Heise (H, 6.6 Ma) and Yellowstone Plateau (YP, 2 Ma). DERP was used in combination with the independent TitaniQ geobarometer to estimate magma storage pressures for four of these eruptive centers (BJ, TF, H and YP). A focus was set to samples from the Twin Falls eruptive center, where a drill core obtained by ICDP project HOTSPOT close to the city of Kimberly, Idaho (USA), allows for a detailed insight into the stratigraphy. Results show that the magma storage pressure is constant within an eruptive complex but decreases with time between different eruptive complexes among the SRPY. Estimated pressures are 351 ± 35 MPa for Bruneau-Jarbidge, 264 ± 31 MPa for Twin Falls, ~230 MPa for Heise and ~140 MPa for Yellowstone Plateau. Reasons for these abrupt deacreases over time might lay in changes of the elastic thickness of the crust in the SRPY and its geometry on its lower side during the interaction with the hot mantle plume.