High harmonics on amplifier output

I have a 868 MHz input signal of around 4dBm with 2nd harmonic of -60dBm and 3rd of -80dBm thanks to a SAW filter. At the output of the ADL5320 I get around 20dBm on my base frequency as expected, but the 2nd harmonic jumps to -20dBm and 3rd to -30dBm - that's 40-50 dB gain for the harmonics. Increasing the voltage from 5V to the maximally allowed 6.5V decreases the harmonics by around 5-7dB. Signal well attenuated at the input of the spectrum analyzer, so not a distortion of the gear. Any advice on what am I possibly missing?