The position of the cotectic curve separating quartz and feldspar stability fields in the rhyolite system Qz–Ab–Or(–An–H2O) depends on pressure, making it a potential geobarometer applicable to high-silica volcanic products if melt water contents (H2Omelt) are known. Until recently, the applicability of this geobarometer has been limited because pressure effects can be largely obscured by the effects of nearly ubiquitous normative anorthite (An, CaAl2Si2O8) in rhyolitic melts. In this study, we present new phase equilibria data that allow us to constrain the position of thermal minima and quartz–sanidine–plagioclase triple points on the quartz–feldspar cotectic curves at various pressures and melt normative An contents. Data were derived by conducting crystallization experiments to determine phase relations at the following conditions: 200 MPa, 1.4 wt % H2Omelt, 3.5 wt % An; 200 MPa, 1.3 wt % H2Omelt, 7 wt % An; 500 MPa, 3 wt % H2Omelt, 3.5 wt % An; 500 MPa, 1.4 wt % H2Omelt, 3.5 wt % An; 500 MPa, 1.3 wt % H2Omelt, 7 wt % An. Using this dataset with published phase equilibria results, we present a geobarometer based on the main parameters influencing cotectic compositions in the rhyolitic system: pressure, H2Omelt and melt An content. Our new geobarometer DERP (DEtermining Rhyolite Pressures) is calibrated to calculate pressures of magma storage from cotectic glass compositions with up to 7 wt % normative melt An. DERP is calibrated for any H2Omelt in the pressure range 50–500 MPa. Its application is restricted to high-silica rhyolitic systems saturated with respect to quartz and feldspar(s). DERP was tested against various independent methods for estimating rhyolite pressures available in the literature (with an overall error of less than 100 MPa). Comparing pressures estimated with DERP and rhyolite-MELTS, which are based on the same approach, suggests that rhyolite-MELTS underestimates the effect of An.