Bandtail states in disordered semiconductor materials result in losses in open-circuit voltage (Voc) and inhibit carrier transport in photovoltaics. For colloidal quantum dot (CQD) films that promise low-cost, large-area, air-stable photovoltaics, bandtails are determined by CQD synthetic polydispersity and inhomogeneous aggregation during the ligand-exchange process. Here we introduce a new method for the synthesis of solution-phase ligand-exchanged CQD inks that enable a flat energy landscape and an advantageously high packing density. In the solid state, these materials exhibit a sharper bandtail and reduced energy funnelling compared with the previous best CQD thin films for photovoltaics. Consequently, we demonstrate solar cells with higher Voc and more efficient charge injection into the electron acceptor, allowing the use of a closer-to-optimum bandgap to absorb more light. These enable the fabrication of CQD solar cells made via a solution-phase ligand exchange, with a certified power conversion efficiency of 11.28%. The devices are stable when stored in air, unencapsulated, for over 1,000 h.