Decrease of the quantum well area should result in a fine structure of its do I-V curve due to either quantization of the 2-D electron motion in the well, or charging of the well by single electrons, or both. What effect dominates, is determined by a parameter α, the same which determines magnitude of the I-V curve hysteresis due to the multi-electron charging of large-area quantum wells. © 1990, Elsevier Science Publishers B.V. (North-Holland). All rights reserved.