The idea of explicit model predictive control (MPC) is to characterize optimal control inputs as an explicit piecewise affine (PWA) function of the initial conditions. The function, however, is often too complex and either requires too much processing power to evaluate on-line, or consumes a prohibitive amount of memory. The paper focuses on the memory issue and proposes a novel method of replacing a generic continuous PWA function by a different function of significantly lower complexity in such a way that the simple function guarantees the same properties as the original. The idea is based on eliminating 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.