High peak-to-average power ratio (PAPR) of transmitted signals is a major drawback for multi-carrier modulation (MCM) systems such as orthogonal frequency division multiplexing (OFDM) and wavelet packet division multiplexing (WPDM). Companding transform is an efficient and simple method to reduce the PAPR for MCM systems. In this paper, a novel adaptive companding transform scheme is proposed to efficaciously reduce the Peak-to-Average Power Ratio of OFDM and WPDM signals. In this technique, only the signals, whose amplitudes are higher than the threshold, are compressed in the transmitter, adaptively. We propose a new formula for the threshold level and send the threshold value to the receiver as side information. Using a simple judgment process, the expanding operation based on the transmitted side information will be executed to the compressed signals in the receiver. Computer simulation results show that the adaptive threshold companding (ATC) scheme effectively improves the performance of PAPR by introducing a simple adaptive threshold judgment process.