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The idea of Explicit Model Predictive Control (MPC) is to find the optimal control input as an explicit Piecewise Affine (PWA) function of the initial conditions. The function, however, is often too complex to be processed by a typical control hardware setup in real time. Therefore the paper proposes a novel method of replacing a generic continuous PWA function by a different function of significantly lower complexity in such a way that optimal closed-loop performance, stability and constraint satisfaction are preserved. The idea is based on eliminating a significant portion of the regions of the PWA function over which the function attains a saturated value. An extensive case study is presented which confirms that a significant reduction of complexity is achieved in general.