In this paper, we investigate an efficient user selection and sub-band allocation algorithm in which each user transmits two-step partial CQI to reduce the amount of feedback in multi-user downlink OFDMA systems. Simulation results show that we can greatly reduce the feedback rate at the expense of negligible performance degradation compared to the full CQI feedback schemes or that we can greatly improve the performance with slightly reduced feedback rate compared to conventional partial CQI feedback schemes.