Polymer solar cells are an exciting class of next-generation photovoltaics, because they hold promise for the realization of mechanically flexible, lightweight, large-area devices that can be fabricated by room-temperature solution processing. High power conversion efficiencies of ∼10% have already been reported in tandem polymer solar cells. Here, we report that similar efficiencies are achievable in single-junction devices by reducing the tail state density below the conduction band of the electron acceptor in a high-performance photoactive layer made from a newly developed semiconducting polymer with a deepened valence energy level. Control over band tailing is realized through changes in the composition of the active layer and the structure order of the blend, both of which are known to be important factors in cell operation. The approach yields cells with high power conversion efficiencies (∼9.94% certified) and enhanced photovoltage.