Access to a wireless network is attempted by sending on a random access channel RACH at a first transmit power a first preamble comprising a signature sequence that is randomly selected from a set of signature sequences. After the access attempt from sending the first preamble is determined unsuccessful, access to the wireless network is re-attempted by sending on the RACH at a second transmit power a second preamble comprising a signature sequence, in which the second transmit power is no greater than the first transmit power. Embodiments variously combine different options: the signature sequences of the first and second preambles are each randomly selected separately, or the signature sequence of the first preamble is re-used in the second preamble; the first and second transmit powers are each equal to an initial transmit power, or the second transmit power is the initial power and less than the first transmit power.