We investigate the charge transport physics of a previously unidentified class of electron-deficient conjugated polymers that do not contain any single bonds linking monomer units along the backbone but only double-bond linkages. Such polymers would be expected to behave as rigid rods, but little is known about their actual chain conformations and electronic structure. Here, we present a detailed study of the structural and charge transport properties of a family of four such polymers. By adopting a copolymer design, we achieve high electron mobilities up to 0.5 cm2 V−1 s−1. Field-induced electron spin resonance measurements of charge dynamics provide evidence for relatively slow hopping over, however, long distances. Our work provides important insights into the factors that limit charge transport in this unique class of polymers and allows us to identify molecular design strategies for achieving even higher levels of performance.