Graphene oxide (GO) is one of the most promising candidates for next generation of atomically thin membranes. Nevertheless, one of the major issues for real world application of GO membranes is their undesirable swelling in an aqueous environment. Recently, we demonstrated that generation of H3O+ and OH- ions (e.g., with an external electric field) in the interlayer gallery could impart aqueous stability to the layered GO membranes (A. Gogoi, ACS Appl. Mater. Interfaces, 2022, 14, 34946). This, however, compromises the water flux through the membrane. In this study, we report on reducing the GO nanosheets as a solution to this issue. With the reduction of the GO nanosheets, the water flux through the layered GO membrane initially increases and then decreases again beyond a certain degree of reduction. Here, two key factors are at play. Firstly, the instability of the H-bond network between water molecules and the GO nanosheets, which increases the water flux. Secondly, the pore size reduction in the interlayer gallery of the membranes, which decreases the water flux. We also observe a significant improvement in the salt rejection of the membranes, due to the dissociation of water molecules in the interlayer gallery. In particular, for the case of 10% water dissociation, the water flux through the membranes can be enhanced without altering its selectivity. This is an encouraging observation as it breaks the traditional tradeoff between water flux and salt rejection of a membrane.