Efficient conjugated polymer optoelectronic devices benefit from concomitantly high luminescence and high charge carrier mobility. This is difficult to achieve, as interchain interactions, which are needed to ensure efficient charge transport, tend also to reduce radiative recombination and lead to solid-state quenching effects. Many studies detail strategies for reducing these interactions to increase luminescence, or modifying chain packing motifs to improve percolation charge transport; however achieving these properties together has proved elusive. Here, we show that properly designed amorphous donor-alt-acceptor conjugated polymers can circumvent this problem; combining a tuneable energy gap, fast radiative recombination rates and luminescence quantum efficiencies >15% with high carrier mobilities exceeding 2.4 cm2/Vs. We use photoluminescence from exciton states pinned to close-crossing points to study the interplay between mobility and luminescence. These materials show promise towards realising advanced optoelectronic devices based on conjugated polymers, including electrically-driven polymer lasers.