In rate-adaptive orthogonal frequency division multiplexing (OFDM) systems, limited feedback schemes are essential to reduce the number of subchannels for which the channel state information is fed back by the users. For the practically important best-M scheme, in which each user feeds back only its M strongest subchannels and their indices to the base station (BS), we derive a throughput-optimal rate adaptation policy that enables the BS to assign rates to the subchannels of every user. We present it in closed-form for the widely used exponential correlation model. The novelty of the policy lies in its exploitation of the structure of the information fed back by the best-M scheme and the correlation among subchannel gains. We also present a near-optimal, lower computational complexity approach. In effect, our approach facilitates rate adaptation and scheduling by the BS even on subchannels that are not fed back by a user due to feedback constraints. For various schedulers, we show that it improves the downlink throughput compared to several conventional approaches, without requiring any additional feedback. © 2016 IEEE.