The operation of racetrack memories is based on the motion of domain walls in atomically thin, perpendicularly magnetized nanowires, which are interfaced with adjacent metal layers with high spin-orbit coupling. Such domain walls have a chiral Néel structure and can be moved efficiently by electrical currents. High-capacity racetrack memory requires closely packed domain walls, but their density is limited by dipolar coupling from their fringing magnetic fields. These fields can be eliminated using a synthetic antiferromagnetic structure composed of two magnetic sub-layers, exchange-coupled via an ultrathin antiferromagnetic-coupling spacer layer. Here, we show that nanosecond-long current pulses can move domain walls in synthetic antiferromagnetic racetracks that have almost zero net magnetization. The domain walls can be moved even more efficiently and at much higher speeds (up to ∼750 m s-1) compared with similar racetracks in which the sub-layers are coupled ferromagnetically. This is due to a stabilization of the Néel domain wall structure, and an exchange coupling torque that is directly proportional to the strength of the antiferromagnetic exchange coupling between the two sub-layers. Moreover, the dependence of the wall velocity on the magnetic field applied along the nanowire is distinct from that of the single-layer racetrack due to the exchange coupling torque. The high domain wall velocities in racetracks that have no net magnetization allow for densely packed yet highly efficient domain-wall-based spintronics.