The authors report on electron interference effects in n-Hg_0.8Cd_0.2Te (CMT). This narrow-gap semiconductor has a very light effective electron mass and a comparatively long electron wave coherence length. Due to these properties a non-classical conductivity was observed in bulk samples at elevated temperatures up to 35 K. Dimensional crossovers were discovered in samples as large as 1*2.5* 35 mu m³: with decreasing temperature size-quantization from three- via two- to one-dimensional behaviour takes place. The evidence of pronounced electron wave interference effects favours CMT as a candidate for novel quantum size devices, as cutoff wavelength transistors or quantum-valve infrared detectors.