This article presents a demonstration of the improved performance of an X-ray free-electron laser (FEL) using the optical klystron mechanism and helical undulator configuration, in comparison with the common planar undulator configuration without optical klystron. The demonstration was carried out at Athos, the soft X-ray beamline of SwissFEL. Athos has variable-polarization undulators, and small magnetic chicanes placed between every two undulators to fully exploit the optical klystron. It was found that, for wavelengths of 1.24 nm and 3.10 nm, the required length to achieve FEL saturation is reduced by about 35% when using both the optical klystron and helical undulators, with each effect accounting for about half of the improvement. Moreover, it is shown that a helical undulator configuration provides a 20% to 50% higher pulse energy than planar undulators. This work represents an important step towards more compact and high-power FELs, rendering this key technology more efficient, affordable and accessible to the scientific community.