Electrical conductivities of molten Hawaiian tholeiite and Crater Lake andesite were measured between 1200 ¿C and 1400 ¿C at atmospheric pressure and at pressures up to 17 and 25 kbar, respectively. Isobaric plots of log &sgr; versus 1/T (&sgr; is electrical conductivity) are linear, with the exception of the zero pressure tholeiite melt data. Conductivities decrease with increasing pressure in both melts, with the andesitic melt exhibiting a greater pressure dependence. Between 5 and 10 kbar, abrupt decreases in the slopes of isothermal log &sgr; versus P plots (i.e., decreases in activation volume) are observed for both rock melts. This discontinuity probably reflects changes in melt structure, as opposed to changes in conduction mechanism. In each pressure range, the data for each rock melt can be described reasonably well by an equation of the form &sgr;=&sgr;'0 exp<-(Ea+PΔV&sgr;) /kT>, where &sgr;'0 is a preexponential constant, Ea is the activation energy, and ΔV&sgr; is the activation volume. A qualitative model involving depolymerization of the melt with increased pressure leading to increased efficiency of packing can explain the observed discontinuity in activation volume as well as the observed pressure dependences of other melt physical properties such as viscosity and density. Conductivity versus melt fraction curves for partially molten peridotite are reevaluated using high pressure tholeiitic melt conductivities and crystalline conductivity values recently determined by other workers. Minimum melt fraction estimates of 5--10% are required to explain upper mantle regions of anomalously high electrical conductivity in terms of a partial melting hypothesis.