The Poole–Frenkel effect is commonly used to decide between donorlike and acceptorlike electronic character for deep‐level defects in semiconductors. However, there exists at least one defect, the EL2 center in GaAs, which is experimentally established to be a deep donor and yet does not exhibit the classical Poole–Frenkel effect for thermal emission of electrons. In this communication it is proposed that the existence of another well‐documented deep‐level phenomenon can suppress the Poole–Frenkel effect. Namely, a thermally activated capture cross section, which identifies an energy barrier to carrier capture and is commonly ascribed to a multiphonon emission process, introduces additional mechanisms which can alter the predominance of the Coulombic potential of the emitted carrier so as to suppress the electric‐field‐induced barrier lowering. A simple one‐dimensional model is analyzed to qualitatively illustrate the combined phenomena.