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This paper introduces a new, accurate, and complexity-reduced three-nonlinear-box model that is suitable for the behavioral modeling and digital predistortion (DPD) of power amplifiers (PAs) exhibiting memory effects. This model is composed of a look-up table (LUT), a memory polynomial (MP), and an envelope MP (EMP), which are all connected in parallel, and it is termed as Parallel-LUT-MP-EMP (PLUME). The PLUME model's performance is experimentally assessed using a highly nonlinear Doherty PA driven by a multicarrier wideband code division multiple access signal. A comparison is held between the PLUME model and different state-of-the-art models reported in the literature, such as the MP model, the parallel twin nonlinear two-box model, and the generalized MP (GMP) model. The experimental results, in both behavioral modeling and DPD applications, demonstrate that the proposed PLUME model outperforms the first two models. However, it shows the same accuracy as the GMP model but with an approximately 45% reduction in the number of coefficients. This significant decrease in coefficients considerably reduces the model computational complexity. Another comparison of the resources utilized for field programmable gate array implementation of the PLUME model and the GMP model is performed, which reveals that the PLUME model uses much fewer resources than the other model.