We have found that in modulation-doped CdTe/Cd 1--x Mg x Te : I heterostructures a non-intentional formation of a potential valley outside the quantum well in the region doped with iodine donors is the origin of parallel transport. We have shown the rules how to choose the parameters of the quantum structure in order to eliminate this phenomenon. Electrical measurements performed on specially designed samples, which had parameters of the quantum structure fulfilling the mentioned rules, showed the formation of two-dimensional electron gas without parallel electron transport.Introduction Parallel transport in low-dimensional semiconductor systems is a parasitic phenomenon, which can strongly influence their electrical properties. For example, in modulation-doped GaInAs/AlInAs and CdTe/CdMnTe heterostructures [1, 2] large parallel conduction often prevents the observation of the quantum Hall effect (QHE) and makes the characterization of two-dimensional electron gas (2DEG) very difficult. In our previous papers [3,4] we have shown that also in the CdTe/Cd 1--x Mg x Te single quantum well heterostructures the parallel transport often occurs in spite of high material quality. The elimination of this phenomenon in low-dimensional II-VI structures is necessary for their possible application in light emitting devices or in hybrid optoelectronics as spin injectors.In the present paper: 1. we have systematically studied the electrical properties of a number of MBE-grown modulation-doped CdTe/Cd 1--x Mg x Te : I heterostructures having various parameters of the quantum structure and 2. we performed theoretical calculations of potential profiles of the heterostructures in order to solve the above-mentioned problem and thus to find such parameters of the samples for which high quality 2DEG in the quantum well is formed without any parallel conduction.