Donor–acceptor organic solar cells often show high quantum yields for charge collection, but relatively low open-circuit voltages (V) limit power conversion efficiencies to around 12%. We report here the behavior of a system, PIPCP:PC$\mathrm{<mrow\; data-mjx-texclass="ORD">61</mrow>}$BM, that exhibits very low electronic disorder (Urbach energy less than 27 meV), very high carrier mobilities in the blend (field-effect mobility for holes >10$\mathrm{<mrow\; data-mjx-texclass="ORD">-2</mrow>}$ cm$\mathrm{<mrow\; data-mjx-texclass="ORD">2</mrow>}$ V$\mathrm{<mrow\; data-mjx-texclass="ORD">-1</mrow>}$ s$\mathrm{<mrow\; data-mjx-texclass="ORD">-1</mrow>}$), and a very low driving energy for initial charge separation (50 meV). These characteristics should give excellent performance, and indeed, the V is high relative to the donor energy gap. However, we find the overall performance is limited by recombination, with formation of lower-lying triplet excitons on the donor accounting for 90% of the recombination. We find this is a bimolecular process that happens on time scales as short as 100 ps. Thus, although the absence of disorder and the associated high carrier mobility speeds up charge diffusion and extraction at the electrodes, which we measure as early as 1 ns, this also speeds up the recombination channel, giving overall a modest quantum yield of around 60%. We discuss strategies to remove the triplet exciton recombination channel.