AbstractGas-filled hollow-core fiber (HCF) pulse post-compressors generating few- to single-cycle pulses are a key enabling tool for attosecond science and ultrafast spectroscopy. Achieving optimum performance in this regime can be extremely challenging due to the ultra-broad bandwidth of the pulses and the need of an adequate temporal diagnostic. These difficulties have hindered the full exploitation of HCF post-compressors, namely the generation of stable and high-quality near-Fourier-transform-limited pulses. Here we show that, independently of conditions such as the type of gas or the laser system used, there is a universal route to obtain the shortest stable output pulse down to the single-cycle regime. Numerical simulations and experimental measurements performed with the dispersion-scan technique reveal that, in quite general conditions, post-compressed pulses exhibit a residual third-order dispersion intrinsic to optimum nonlinear propagation within the fiber, in agreement with measurements independently performed in several laboratories around the world. The understanding of this effect and its adequate correction, e.g. using simple transparent optical media, enables achieving high-quality post-compressed pulses with only minor changes in existing setups. These optimized sources have impact in many fields of science and technology and should enable new and exciting applications in the few- to single-cycle pulse regime.