The potential gains of multiple antennas in wireless systems can be limited by the channel state information imperfections. In this context, this paper tackles the feedback in multiuser correlated multiple input single output (MU-MISO). We propose a framework to feedback the minimum number of bits without performance degradation. This framework is based on decorrelating the channel state information by compression and then quantize the compressed (CSI) and feedback it to the base station (BS). We characterize the rate loss resulted from the proposed framework. An upper bound on the rate loss is derived in terms of the amount of feedback and the statistics of the channel. Based on this characterization, we propose am adaptive bit allocation algorithm that takes into the account the channel statistics to reduce the rate loss induced by the quantization. Moreover, in order to maintain a constant rate loss with respect to the perfect CSIT case, it is shown that the number of feedback bits should scale linearly with the SNR (in dB) and to the rank of the user transmit correlation matrix. We validate the proposed framework by Monte-carlo simulations.