Due to the fact that impurities normally change their doping characters when they undergo shallow to deep transitions or deep‐to‐false‐valence transitions, a single defect, such as a cation on an Sb site, can explain all of the following facts for nonintentionally doped AlxGa1−xSb alloys and InAs/AlxGa1−xSb superlattices and quantum‐well structures: (i) Bulk GaSb isptype; (ii) bulk AlSb is semi‐insulating; (iii) InAs/AlSb superlattices with InAs quantum wells thicker than a critical thicknessdc(x=1.0) arentype, where the InAs shallow–deep critical thickness functiondc(x) is around &bartil;100–&bartil;150 A˚ for 0.5<x≤1.0 for InAs/AlxGa1−xSb superlattices; (iv) InAs/AlSb superlattices with InAs quantum wells thinner thandc(x=1.0) are semi‐insulating. In addition, the theory predicts that Al0.5Ga0.5Sb and AlSb will be semi‐insulating when nonintentionally doped, but can be converted toptype by the application of hydrostatic pressureP:P≳90 kbar andP≳150 kbar, respectively. These changes of doping character, which lie outside the conventional effective‐mass theory, occur often in type‐II band‐alignment systems, such as InAs/AlxGa1−xSb.