The accurate and precise determination of the compositions of silicate glasses formed from melts containing volatile components H2O and CO2 recovered from high-pressure, high-temperature experiments is essential to our understanding of geodynamic processes taking place within the planet. Silicate melts are often difficult to analyze chemically because the formation of quench crystals and overgrowths on silicate phases is rapid and widespread upon quenching of experiments, preventing the formation of glasses in low-SiO2 and volatile-rich compositions. Here, we present experiments conducted in a novel rapid quench piston cylinder apparatus on a series of partially molten low-silica alkaline rock compositions (lamproite, basanite, and calk-alkaline basalt) with a range of water contents between 3.5 and 10 wt%. Quench modification of the volatile-bearing silicate glasses is significantly reduced compared to those produced in older piston cylinder apparatuses. The recovered glasses are almost completely free of quench modification and facilitate the determination of precise chemical compositions. We illustrate significantly improved quench textures and provide an analytical protocol that recovers accurate chemical compositions from both poorly quenched and well-quenched silicate glasses.