A simple and flexible technique for improving the modeling and predistortion of power amplifiers is presented. The technique, which relies on the sparsity assumption for the kernel coefficients of the full Volterra (FV) behavioral model, combines a greedy algorithm for the selection of the active coefficients, a maximum likelihood method for their estimation and an information criterion for determining the best model. The approach has been applied to the design of reduced-parameters FV-based digital predistorters for three power amplifiers driven with orthogonal frequency division multiplexing signals, following the LTE and DVB-T2 standards, and a multichannel wideband code-division multiple access signal. Results show that the proposed linearizers meet the spectral masks and error vector magnitude constraints of the referred standards and provide a reduction better than 45% in the number of parameters, compared to the FV predistorters.