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This letter investigates the problem of user selection with adaptive multilevel modulation for a single-carrier frequency division multiple access system with iterative multiuser detection. Multiple users sharing a common set of subcarriers, called a chunk, cause multiple access interference (MAI) which degrades quality-of-service (QoS). To guarantee QoSs of the users and achieve multiuser diversity, the proposed algorithm allocates each chunk to users with favorable channel conditions. However, despite this user scheduling, the improvement of spectral efficiency is limited at high SNR due to the MAI. In order to effectively mitigate MAI, we employ adaptive multilevel modulation which adjusts the number of layers at each user selection. Simulation results show that the proposed algorithm improves spectral efficiency compared to conventional algorithms.