In this work, we analyze opportunistic beamforming with finite number of single-antenna users under the constraint that the feedback overhead from the mobiles to the base is constant. First, we characterize the impact of the fading variances of the users and the spatial correlation on the sum rate of TDMA based opportunistic beamforming using majorization theory. Further, we describe quantitatively the high-SNR behavior in terms of throughput slope and power offset. Next, the impact of the fading variances of the users on an upper bound of the sum rate for space division multiple access (SDMA) based opportunistic beamforming is derived which is tight for high SNR. We propose to adapt the number of active beams to the SNR and the number of active users in a cell and illustrate the corresponding optimization problem by simulations.