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The density of silicate melts at high pressure determined the efficiency of gravitational differentiation in the solidifying magma ocean and thus the starting conditions for the Earth's evolution, it controls the migration of melts in the lithosphere and their stabilization in the transition zone and near the core mantle boundary. Yet, no density systematic exists for melts across the pressure range of the mantle. This is primarily because of severe experimental difficulties associated with measuring the density of silicate liquids at mantle pressures and temperatures (tiny sample size, melt chemical reactivity, lack of crystalline structure). The use of glasses as proxies of melts at high pressure lifts some but not all of these challenges, and may be important in developing theoretical models of melts physical behavior at high pressures. Here we report on the density of MORB glass up to 32.3 GPa at room temperature measured by the recently developed all-optical method in a diamond anvil cell. The comparison of the MORB glass density to that for other basaltic glasses reported in the literature reveals contradictions, similarly to those existing between data available for MORB-like melts, which underscore the need for consistent systematic melt and glass density measurements at high pressure across a broad compositional space. More broadly, the compression behavior of MORB and other basaltic glasses, SiO2, MgSiO3, and Mg2SiO4 glasses tentatively shows that the incorporation of SiO2 and/or large network-modifiers (larger than Mg) softens the glass (smaller isothermal bulk modulus and its pressure derivative). Future all-optical measurements of glass density may provide fundamental, critical input to develop models of complex glasses and melts physical properties, and hopefully help assessing the solidification of the primordial magma ocean, the initiation and development of physical and chemical heterogeneity in the mantle, and the migration or stabilization of melts at different levels in the deep Earth.