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IEEE 802.11ax stations can use multi-user (MU) uplink OFDMA-based random access (UORA) to improve per-station throughput in dense deployments in comparison to legacy IEEE 802.11 single-user access. Unfortunately, UORA suffers from a high collision probability and low efficiency under high contention. In this paper, we address this problem by modifying the UORA backoff selection method. The proposed solution allows an access point to adjust the OFDMA random access backoff (OBO) countdown rate to decrease the probability of uplink transmission failures. The implemented changes considerably improve UORA performance. We show through extensive simulations, that the proposed efficient OFDMA random access backoff (E-OBO) ensures throughput, efficiency, and collision probability close to optimal and outperforms state-of-the-art solutions.