FM-to-AM conversion is an important issue that could prevent fusion ignition with high-power lasers, such as the Laser MegaJoule (LMJ). We first overview the whole problem of FM-to-AM conversion in high-power lasers and we explain why AM spectral content of FM-to-AM conversion is important, although this information was not used in previous studies. We then propose simple analytical models to simulate FM-to-AM conversion in the LMJ frequency conversion system. We succeed in isolating every cause of spectrum distortion and give, for each of them, FM-to-AM predictions that are in very good agreement with simulations of a complex propagation code. Finally, we show how the last grating filters most of the FM-to-AM conversion. We conclude that the FM-to-AM conversion distortion criterion will be, on LMJ, below 40% in the last optics and 10% on the target.