In multiuser OFDMA FDD systems with resource allocation based on the instantaneous channel quality of the users, the feedback overhead can be very large. In this paper, a method to significantly reduce this feedback is proposed. The idea is to let the users feed back the channel quality (the SNR in this paper) of only a sub-set of their strongest sub-carriers. The SNRs on the other sub-carriers are instead estimated from the fed back values. We derive the MMSE estimator of the SNR of a sub-carrier, which uses two fed back SNRs as input. As a comparison, we also study the performance of the LMMSE estimator as well as spline interpolation. Numerical results show that the LMMSE estimator tends to underestimate the SNR compared to the other two estimators, whereas the interpolation tends to overestimate the SNR. System simulations including adaptive modulation and packet losses indicate that the MMSE estimator is the best choice in practice.