A radio terminal is organized to send a first access signal then, when it receives a positive acknowledgement from a base station, a second access signal, resources of the communication network being allocated to the radio terminal after receipt of the said second access signal at the base station. At a base station, the first access signal sent by a radio terminal is received and the communication service requested by the terminal is detected therein. In conditional manner, depending on the detected communication service, a receive power of the first access signal is measured, the measured receive power is compared with a threshold, and the transmission of a positive acknowledgement of the first access signal to the radio terminal is inhibited, when the measured receive power is greater than the said threshold.