The effect of cluster size, oxidation state, and the support upon the structures and energetics of subnanometer palladium nanoparticles is investigated within a density functional framework. Gas phase global minima of Pd4 and Pd10 along with their suboxide counterparts are determined using a genetic algorithm and deposited upon MgO (001) and a high-index alumina surface. It is observed that there is an oxidation-dependent transition in the smaller clusters from three-dimensional to two-dimensional structures both in the gas phase and when supported by a surface. MgO strongly promotes a change from tetrahedral- and icosahedral-based structures toward cubic forms, while alumina induces significant distortion of the cluster and the breaking of Pd–Pd bonds. Increased oxygenation contributes cooperatively to these effects, causing disruption of the Pd–Pd bond network, favoring the incorporation of oxygen into the cluster structure, further complicating unambiguous structure prediction.