In certain circumstances, a mobile radiocommunication terminal estimates an initial radio signal transmission power, i.e. a random access request, to a base station located within the range thereof. If it is very close to said station, said initial estimated power can be lower, even greatly lower, than the minimum transmission power of the mobile terminal. In order to limit interference with other communications in progress, the transmission of said signals is inhibited if the difference between the minimum transmission power and the initial estimated power lies beyond a predefined threshold.