In this paper, we present the cube coefficient subspace (CCS) architecture for linearizing power amplifiers (PAs), which divides the overparametrized Volterra kernel into small, computationally efficient subkernels spanning only the portions of the full multidimensional coefficient space with the greatest impact on linearization. Using measured results from a Q-Band solid state PA, we demonstrate that the CCS predistorter architecture achieves better linearization performance than state-of-the-art memory polynomials and generalized memory polynomials.