Abstract The spin filtering through Cd 1− y Mg y Te/Cd 1− x Mn x Te heterostructure, both with zero and with positive zero-field conduction band offset, is investigated theoretically. The magnetic field dependence of the transmission coefficients, current densities, and spin polarizations for considered systems have been studied. It is found that a positive zero-field conduction band offset as high as 3 meV shifts considerably the onset of the spin-up complete suppression to lower magnetic field region and thereby unity spin polarization initiates at lower magnetic field.