We study power loading in a multicarrier system with no more than one bit of feedback per sub-channel. The sub-channels can be correlated and full channel state information is assumed at the receiver. A model with N parallel  two-state (good/bad) sub-channels is first considered, where  the feedback selects a fixed number of sub-channels to activate.   The performance of an optimal vector quantization feedback scheme  for large N is given by a rate distortion function. We characterize the loss in forward rate from the asymptotic (rate-distortion) value as N increases, assuming optimal variable- and fixed-rate feedback codes. We subsequently extend these results to parallel Rayleigh block fading sub-channels, where the feedback designates a set of sub-channels, which are activated with equal power. Numerical results show that the corresponding rate-distortion feedback codes can provide a significant increase in forward rate at low SNRs  relative to simpler feedback schemes based on lossless source coding.