A radio communication system has a random access channel for the transmission of data (214) from a secondary station to a primary station. Such a channel is intended for use by the secondary stations having data (214) to transmit to a primary station while not actually engaged in a call. By enabling access requests (202) to be transmitted with a range of time offsets relative to the boundary (302) of their time slot, a much greater number of degrees of freedom is available to a secondary station requesting access to a random access channel. This enables significantly improved efficiency of resource allocation by increasing the amount of information transmitted to the primary station by the access request (202).