Digital baseband predistortion (DBP) is not particularly well suited to linearizing wideband power amplifiers (PAs); this is due to the exorbitant price paid in computational complexity. One of the underlying reasons for the computational complexity of DBP is the inherent inefficiency of using a sufficiently deep memory and a high enough polynomial order to span the multidimensional signal space needed to mitigate PA-induced nonlinear distortion. Therefore we have developed a new mathematical method to efficiently search for and localize those regions in the multidimensional signal space that enable us to invert PA nonlinearities with a significant reduction in computational complexity. Using a wideband code division multiple access (CDMA) signal we demonstrate and compare the PA linearization performance and computational complexity of our algorithm to that of conventional DBP techniques using measured results.