We demonstrate efficient amplification of few-optical-cycle mid- IR pulses in single-pass continuously pumped laser amplifiers based on polycrystalline Cr2+:ZnS and Cr2+:ZnSe. The 1.7 W output of a Kerr-lens mode-locked master oscillator at 2.4 μm central wavelength, 79 MHz repetition rate was amplified to 7.1 W and 2.7 W in Cr2+:ZnS and Cr2+:ZnSe, respectively. High peak power of the input pulses (0.5 MW) and high nonlinearity of the amplifiers' gain media resulted in a significant shortening of the output pulses and in spectral broadening. Transformlimited 40 fs pulses of the master oscillator were compressed to about 27- 30 fs. The spectrum of the pulses was broadened from 136 nm to 450 nm (at -3 dB level); the span of the spectra exceeds 600 nm at -10 dB level.