This paper investigates the trade-off between the power amplifier (PA) power efficiency and the corresponding digital predistortion (DPD) model complexity needed for its linearization. The linearization performance is estimated with the adjacent channel power ratio (ACPR). A hill-climbing algorithm is proposed to trace approximate Pareto fronts of the ACPR versus the DPD model number of coefficients at different PA operating points (OP). Crest factor reduction is applied when the backoff of the OP is less than the peak-to-average power ratio (PAPR) of the LTE signal. Experimental results on a PA with a Long Term Evolution (LTE) signal give interesting insights on the relation between DPD complexity and PA power efficiency for a given ACPR requirement. Finally we propose a criterion for the trade-off between the PA efficiency and the DPD complexity in function of the ACPR requirement.