Post-pulse-compression is demanded to produce energetic few-cycle pulses. We propose pre-chirp-managed adiabatic soliton compression (ASC) in gas-filled pressure-gradient hollow-core fibers to suppress the detrimental pedestals and therefore significantly improve the compressed pulse quality. We show that two-stage ASC can compress 125 μJ, 130 fs pulses at 2 μm to a nearly two-cycle pulse 15 fs in duration. Our analytical analysis suggests that ASC is in favor of compressing pulses centered at a longer wavelength. As an example, a 280 μJ, 220 fs Gaussian pulse at 4 μm is compressed to 60 fs with minimal pedestals. We expect that the resulting high-quality, energetic few-cycle pulses will find important applications in high-field science.