The modulus of the wave function of an electron bound to a N isoelectronic trap in GaAs1−xPx:N or In1−xGaxP:N is enhanced neark= O because of the presence of the &Ggr; conduction‐band minimum. The band structure enhancement (BSE) and its effect on the quasidirect behavior of indirect GaAs1−xPx:N and In1−xGaxP:N has been investigated as a function of crystal compositionx (x>xc). To evaluate the modulus of the wave function of the trapped electron, the Koster‐Slater one‐band one‐site model has been employed. The effect of BSE on no‐phonon recombination transitions involving the trapped electron is accentuated by orders of magnitude as the crystal composition is changed to bring the &Ggr; conduction‐band minimum,E&Ggr;, near the N‐trap level,EN. Absorption data taken onx= 1.0 andx= 0.53 GaAs1−xPx:N are consistent with the calculated increase in the probability density in the &Ggr; region asE&Ggr;decreases relative toEX. In order to assess the importance of the enhanced recombination probability on the performance of GaAs1−xPxLED's, the internal quantum efficiency has been calculated as a function of crystal composition. This calculation utilizes a model of the electron and hole recombination kinetics at isoelectronic impurities along with the standard band‐to‐band recombination kinetics. The calculated efficiency weighted by the photopic response of the eye agrees with LED brightness data and confirms that the optimum range of crystal compositions in which to fabricate GaAs1−xPx:N LED's is 0.6≤x≤0.8. This result is in good agreement with current GaAs1−xPx:N LED fabrication processes and the optimization procedure on Zn‐diffused planar devices that has arisen empirically. That is, brightness data on state‐of‐the‐art GaAs1−xPx:N and GaP:N Zn‐diffused LED's support the analytical results developed here. The implications of BSE for In1−xGaxP:N LED's are discussed.