This paper presents and discusses two possible real-time digital predistortion (DPD) architectures suitable for envelope tracking (ET) power amplifiers (PAs) oriented at a final computationally efficient implementation in a field programmable gate array (FPGA) device. In ET systems, by using a shaping function is possible to modulate the supply voltage according to different criteria. One possibility is to use slower versions of the original RF signal's envelope in order to relax the slew-rate (SR) and bandwidth (BW) requirements of the envelope amplifier (EA) or drain modulator. The nonlinear distortion that arises when performing ET with a supply voltage signal that follows both the original and the slow envelope will be presented, as well as the DPD function capable of compensating for these unwanted effects. Finally, two different approaches for efficiently implementing the DPD functions, a polynomial-based and a look-up table-based, will be discussed.