The invention relates to methods for adjusting the transmit power utilized by a mobile terminal for uplink transmissions, and to methods for adjusting the transmit power used by a mobile terminal for one or more RACH procedures. The invention is also providing apparatus and system for performing these methods, and computer readable media the instructions of which cause the apparatus and system to perform the methods described herein. In order to allow for adjusting the transmit power of uplink transmissions on uplink component carriers, the invention suggests introducing a power scaling for uplink PRACH transmissions performing RACH procedures on an uplink component carrier. The power scaling is proposed on the basis of a prioritization among multiple uplink transmissions or on the basis of the uplink component carriers on which RACH procedures are performed.