We report on the experimental development of short-tapered chalcogenide-glass rods for mid-infrared supercontinuum generation. Multi-octave spectral broadening of femtosecond laser pulses is demonstrated from 1.6 to 15.6 µm in a 5-cm-long tapered Ge20Se70Te10 rod with a waist diameter of 25 µm. Despite the multimode nature of the optical waveguide used, this work clearly shows the potential of such simple post-processed rods for advancing fiber SC sources with infrared glasses, thereby unlocking new possibilities in terms of coupling efficiency, spectral coverage, and output power.