Applications of magnetic memory devices greatly benefit from ultra-fast, low-power switching. Here we propose how this can be achieved efficiently in a nano-sized synthetic antiferromagnet by using perpendicular-to-the-plane picosecond-range magnetic field pulses. Our detailed micromagnetic simulations, supported by analytical results, yield the parameter space where inertial switching and relaxation-free switching can be achieved in the system. We furthermore discuss the advantages of dynamic switching in synthetic antiferromagnets and, specifically, their relatively low-power switching as compared to that in single ferromagnetic particles. Finally, we show how excitation of spin-waves in the system can be used to significantly reduce the post-switching spin oscillations for practical device geometries.