A method is provided for adapting modulation schemes to changing channel quality with reduced overhead signalling. A remote unit measures the channel quality of a radio channel along which a signal from a base station reached the remote unit. Based on the channel quality, the remote unit determines a desired set of transmission parameters from a list of sets of transmission parameters. The remote unit determines a difference in position within the list between the current set of transmission parameters and the desired set of transmission parameters. The remote unit transmits the difference to the base station, which selects a new set of transmission parameters using the current set of transmission parameters and the difference. The method requires little signalling between the remote unit and the base station, and is particularly beneficial in communication systems employing many sub-carriers, such as OFDM systems.