This study presents for the first time an integrated overview of the linearisation drawbacks in power amplifiers presenting dynamic effects, either short term or long term, which are usually called memory effects. Working on the concept of best memoryless lineariser (BML), a close analysis of adjacent channel and co-channel distortion is also made. It is then proved mathematically and experimentally that the BML for co-channel distortion is different from the one for adjacent channel distortion. Finally, a formal methodology for calculating the BML for non-linearities presenting dynamic effects, based on the higher order statistics (HOS) tool, is presented.