A method is demonstrated to prepare graphene dispersions at high concentrations, up to 1.2 mg mL(-1), with yields of up to 4 wt% monolayers. This process relies on low-power sonication for long times, up to 460 h. Transmission electron microscopy shows the sonication to reduce the flake size, with flake dimensions scaling as t(-1/2). However, the mean flake length remains above 1 microm for all sonication times studied. Raman spectroscopy shows defects are introduced by the sonication process. However, detailed analysis suggests that predominantly edge, rather than basal-plane, defects are introduced. These dispersions are used to prepare high-quality free-standing graphene films. The dispersions can be heavily diluted by water without sedimentation or aggregation. This method facilitates graphene processing for a range of applications.