This paper deals with spreading sequences selection for downlink and uplink Multi-Carrier Code Division Multiple Access (MC-CDMA) systems with the aim of minimizing the dynamic range of the transmitted multicarrier signal envelope and the multiple access interference. The crest factor of orthogonal and non-orthogonal sequences are compared analytically and by simulation for downlink and uplink phase shift keying MC-CDMA transmissions. Then, in order to minimize the multiple access interference produced by frequency selective channels, an optimized spreading sequence allocation procedure is presented. Finally, a selection of the spreading codes which jointly reduces the multiple access interference and the crest factor is proposed for downlink MC-CDMA systems.