In this paper, we address the challenge of high device density performing simultaneous transmissions by proposing and evaluating a solution to efficiently handle the initial access contention for highly dense LTE networks. We present the implementation of a tree-splitting algorithm in the access procedure of LTE, which is capable to cope with high number of simultaneous arrivals. Based on simulations we show a feasible implementation capable to achieve, under certain network configuration conditions, up to 85% average access delay reduction and 40% reduction on the average energy consumption, while maintaining a consistently low blocking probability, regardless of the number of initial simultaneous access attempts.