Graphene oxide membranes show exceptional molecular permeation properties, with promise for many applications. However, their use in ion sieving and desalination technologies is limited by a permeation cutoff of ∼9 Å (ref. 4), which is larger than the diameters of hydrated ions of common salts. The cutoff is determined by the interlayer spacing (d) of ∼13.5 Å, typical for graphene oxide laminates that swell in water. Achieving smaller d for the laminates immersed in water has proved to be a challenge. Here, we describe how to control d by physical confinement and achieve accurate and tunable ion sieving. Membranes with d from ∼9.8 Å to 6.4 Å are demonstrated, providing a sieve size smaller than the diameters of hydrated ions. In this regime, ion permeation is found to be thermally activated with energy barriers of ∼10-100 kJ mol-1 depending on d. Importantly, permeation rates decrease exponentially with decreasing sieve size but water transport is weakly affected (by a factor of <2). The latter is attributed to a low barrier for the entry of water molecules and large slip lengths inside graphene capillaries. Building on these findings, we demonstrate a simple scalable method to obtain graphene-based membranes with limited swelling, which exhibit 97% rejection for NaCl.