Since the invention of the first magnetic memory disk in 1954, much effort has been put into enhancing the speed, bit density and reliability of magnetic memory devices. In the case of magnetic random access memory (MRAM) devices, fast coherent magnetization rotation by precession of the entire memory cell is desired, because reversal by domain-wall motion is much too slow. In principle, the fundamental limit of the switching speed via precession is given by half of the precession period. However, under-critically damped systems exhibit severe ringing and simulations show that, as a consequence, undesired back-switching of magnetic elements of an MRAM can easily be initiated by subsequent write pulses, threatening data integrity. We present a method to reverse the magnetization in under-critically damped systems by coherent rotation of the magnetization while avoiding any ringing. This is achieved by applying specifically shaped magnetic field pulses that match the intrinsic properties of the magnetic elements. We demonstrate, by probing all three magnetization components, that reliable precessional reversal in lithographically structured micrometre-sized elliptical permalloy elements is possible at switching times of about 200 ps, which is ten times faster than the natural damping time constant.