We investigated the carrier-envelope phase (CEP) stability of hollow-fiber compression for high-energy few-cycle pulse generation. Saturation of the output pulse energy is observed at 0.6 mJ for a 260 μm inner-diameter, 1 m long fiber, statically filled with neon. The pressure is adjusted to achieve output spectra supporting sub-4-fs pulses. The maximum output pulse energy can be increased to 0.8 mJ by either differential pumping (DP) or circularly polarized input pulses. We observe the onset of an ionization-induced CEP instability, which saturates beyond input pulse energies of 1.25 mJ. There is no significant difference in the CEP stability with DP compared to static-fill.