Accommodating Machine-to-Machine applications and their requirements is one of the challenges on the way from LTE towards 5G networks. The envisioned high density of devices, alongside with their sporadic and synchronized transmission patterns, might create signaling storms and overload in the current LTE network. Here, we address the notorious random access (RA) challenge, namely, scalability of the radio link connection establishment protocol in LTE networks. We revisit the binary countdown technique for contention resolution (BCCR), and apply it to the LTE RA procedure. We analytically investigate the performance gains and trade-offs of applying BCCR in LTE. We further simulatively compare BCCR RA with the state-of-the-art RA techniques, and demonstrate its advantages in terms of delay and throughput.