The linearity and power efficiency are two main factors of power amplifiers (PA), which can hardly be improved together. Digital predistortion (DPD) compensates for nonlinearity and memory effects of PAs in high efficiency zone. However, for advanced communication standards the high peak-to-average power ratio of the modulated signal constrains the PA operating point and thus limits the power efficiency. Crest factor reduction (CFR) techniques are applied to address this problem though they degrade the PA linearity relatively. In this paper, we compare different CFR approaches with respect to their performances in terms of linearity, PA power efficiency, and computational complexity. Classical hard clipping, clip-and-filter as well as joint CFR/DPD methods are considered. To complete the comparison, we propose a modeled CFR identified using indirect learning architecture combined with DPD. The simulation results validate its effectiveness on the trade-off among linearity, PA power efficiency and CFR computational complexity.