The power conversion efficiency (PCE) of single junction organic solar cells has increased significantly during the last decade and now approaching the threshold considered necessary for commercialisation. During this period, the structural diversity of semiconducting donor polymers for solar cells has increased dramatically, enabling accelerated development of bulk heterojunction (BHJ) organic solar cells based on polymer donor materials and molecular fullerene derivatives. However both the fullerenes, and the low bandgap polymers typically suffer from low absorption coefficients due to weak oscillator strength. Our approach is to use P3HT as a p-type hole acceptor, and design highly absorbing, low-bandgap n-type small molecules to replace fullerenes. These fullerene acceptors not only have weak absorption, but also poor tunability of absorption over the longer wavelengths of the solar spectrum; morphological instability in thin film blends over time; high synthetic costs and limited scope for synthetic control over electronic and structural properties. For these reasons, we have developed new, synthetically simple electron acceptor materials, based on rhodanine end groups, which have much larger absorption coefficients than fullerenes, coupled with high lying LUMO energy levels, to maximize cell voltages. In BHJ devices with P3HT donor polymer, the rhodanine molecules were demonstrated to outperform fullerenes. The highest performing P3HT devices have power conversion efficiencies approaching 8%, based on a ternary blend of two rhodanine acceptors. We also demonstrate performances of over 12% with one non-fullerene acceptors in combination with lower bandgap polymers, deposited from non-chlorinated solvents.