We present the extension of high-power pulse compression deeper into the challenging IR spectral range around 3.2 μm wavelength, where the effects of material absorption, dispersion, and free electron disturbance on nonlinear propagation become increasingly limiting parameters. 5 mJ, 80 fs pulses from a KTA parametric amplifier were spectrally broadened in a large-core hollow fiber with argon as the nonlinear medium. Subsequent compression through anomalous dispersion in CaF2 yielded 2.5 mJ close-to-transform-limited two-cycle pulses exhibiting a passively stabilized carrier envelope phase (CEP). Furthermore, we outline the feasibility of generating sub-two-cycle pulses with good spatial and temporal characteristics.