In an OFDM transmitter, the input signal is modified in several different ways by sign switches (22) operating on sub-bands generated by a splitter (20). An inverse fast Fourier transform circuit (14) generates an output for each of all the possible types of modification producing a plurality of candidate signals. The signal of best quality is selected by subjecting the candidate signals to processing in a model (54) representing the transmitter amplifier (16), and estimating the candidate signal of best quality determined by a clip energy estimator (58) and/or a low-level estimator (60). A control circuit (64) then causes the transmitter to transmit the candidate signal of best quality together with signalling information indicating the corresponding setting of the sign switches (22).