The coherence of the precessional switching was compared in planar spin-valves comprising either an additional simple perpendicular polarizer or a synthetic antiferromagnet perpendicular polarizer. A significant improvement in the precession coherence was observed experimentally in the second type of samples. Micromagnetic simulations were performed to study the effect of the stray field from the perpendicular polarizer. They provide an explanation for the gradual loss of coherence of the precession in terms of vortex formation, which occurs much faster when a simple perpendicular polarizer is used.