Recent experiments demonstrate that solution-precipitation (pressure-solution) processes in the liquid basalt-olivine system are exceedingly rapid. The effect of liquid basalt on the diffusional (Newtonian) creep rate of polycrystalline olivine is significant; fine-grained, chemically and texturally equilibrated, partially molten assemblages of olivine plus basalt deform at rates which are a factor of 2--5 faster than polycrystalline olivine specimens without the liquid basalt second phase. Measured values of the activation energy for creep suggest that while the kinetics of deformation in this partially molten system are affected by short-circuit diffusion through melt-filled triple junctions, the deformation process is rate-limited by matter transport through melt-free grain boundaries. A simple geometrical model, based on a dynamic equilibrium partial-melt morphology which consists of melt-free olivine grain boundaries coupled with an interconnected melt network along triple junction channnels, adequately describes our deformation results. The extent to which the liquid phase penetrates from the triple junctions into the grain boundaries of texturally equilibrated partial melts determines the contribution of solution-precipitation mechanisms to the creep rate; the critical physical parameters, therefore, are those which affect the solid-liquid and solid-solid interfacial energies, such as various composition-related chemical activities in the liquid phase and the composition and spatial distribution of mineral phases in the crystal residuum.