Feedback of channel state information (CSI) enables a multi-carrier transmitter to optimize the power allocation across sub-channels. We consider a single user feedback scheme in which the entire set of sub-channels is evenly divided into smaller groups of sub-channels, and the receiver requests the use of a particular group if the gain of every sub-channel in the group is above a threshold. The transmit power is then uniformly spread across the requested sub-channel groups. The amount of feedback is therefore controlled by the group size and the threshold. For this scheme, given a total power constraint, we characterize how the channel capacity scales with the number of sub-channels N as a function of the feedback rate. We then consider transmission over a block fading channel, assuming that each coherence block contains both feedback and data transmission. We optimize the fraction of feedback overhead as a function of the number of feedback bits per channel use and coherence time. Numerical results show that the asymptotic (large-N) analysis accurately predicts the behavior of finite-size systems of interest.