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In this paper, we present a method to limit the generation of signal peak power at the output of a digital pre-distorter that is applied to a RF power amplifier (PA) operating in strong compression. The method can be considered as a joint crest-factor reduction and digital pre-distortion (DPD). A challenging characteristic of DPD when applied to a PA in strong compression is the generation of relatively high peaks due to the DPD expansion behavior. Such high peaks generation, which may be physically unrealistic, can easily damage the amplification system. Such a phenomenon, referred in this study as DPD-avalanche, is more noticed when the signal exciting the PA is compressed due to crest-factor reduction. The suggested method for controlling such DPD-avalanche is based on shaping the input signal to the DPD in such a way to keep the pre-distorted signal peak power below or near the maximum allowed peak power of the PA. The suggested method is tested experimentally on a Class-AB and a Doherty PA when excited with a wideband orthogonal frequency-division multiplexing (OFDM) signal. Scenarios for an OFDM signal with and without crest-factor reduction are evaluated. Measurement results when using the proposed DPD-avalanche controller show smooth deterioration of the in-band and out-of-band linearity compared to steep deterioration when no controller is used. In addition, the suggested controller offers a higher operating power range of the DPD while fulfilling out-of-band distortion requirements and preserving low in-band error.