High Peak to Average Power Ratio (PAPR) of the transmitted signal is a serious problem in multicarrier modulation systems. In this paper a new technique for reduction in PAPR of the Multicarrier Code Division Multiple Access (MC CDMA) signals based on combining the Discrete Transform either Discrete Cosine Transform (DCT) or multi-resolution Discrete Wavelet Transform (DWT) with companding is proposed. It is analyzed and implemented using MATLAB. Simulation results of reduction in PAPR and power Spectral Density (PSD) of the MC CDMA with companding and without companding are compared with the MC CDMA with DCT and companding, DWT and companding systems. The new technique proposed is to make use of multi-resolution DWT in combination with companding in order to achieve a very substantial reduction in PAPR of the MC CDMA signal.