Volcanic activity away from plate boundaries occurs in a variety of settings. Linear, age-progressive volcanic chains have been explained as the manifestation of fixed hot spots, possibly generated by plumes originating deep in the mantle. However, important examples of oceanic intraplate volcanism cannot be explained in this way, including short-lived chains and chains violating the predicted age-distance behavior. Furthermore, a significant fraction of volcanism does not occur in linear chains, and observations suggest control by lithosphere structure in many cases. In this study, melting in mantle upwellings that result from the buoyancy associated with the melting itself is considered as a mechanism of intraplate volcanism. Numerical models of this buoyant decompression melting in a layer that is initially at its melting temperature over some depth range are used to determine the duration and amount of melting in upwellings which organize from an initially small, random perturbation for a range of model parameters. A predicted inverse correlation between the amount of melt produced and the duration of melting may be diagnostic of the buoyant melting process. Buoyant melting could occur in a number of geologic settings. Since the oceanic upper mantle may have previously melted beneath a spreading center and subsequently cooled, spontaneous buoyant decompression melting may be possible only in regions where a large-scale mantle upwelling can counteract conductive cooling, keeping the mantle at its solidus temperature over some depth range. Where the mantle is at, or sufficiently near, its solidus, buoyant decompression may spontaneously generate convective storms of melting. This may explain the abundance of volcanism associated with the South Pacific Superswell. Where mantle is slightly cooler than its melting temperature, buoyant melting may not occur spontaneously but may be triggered by some initial upwelling. This may provide a physical explanation for volcanism that is controlled by lithosphere structure.