This paper considers series of azoles (organic compounds whose structure includes benzene, furan, thiophene, oxazole, and oxadiazole cycles chemically coupled with each other) to investigate the dependence of the main lasing characteristics of these compounds (the wavelength and the threshold pump density) on the magnitude of pump-induced triplet losses within the fluorescence band. It is shown that only organic compounds with a definite type of spatial structure satisfy the condition of maximum separation of the band of limiting gain (which coincides with the maximum of the fluorescence band) and the spectra of pump-induced triplet-triplet reabsorption in excited states. The latter condition simultaneously ensures (a) the minimum threshold pump densities required for lasing, (b) hypsochromic shift of the fluorescence band, (c) the maximum fluorescence quantum yield, and (d) the invariance of the ratio γA/τA = const in different solvents. In LCAO MO CSF CI quantum-chemical models, this phenomenon is attributed to the fact that only certain compounds of bisoxazoles, oxadizoles, oxazolyls, and oxadiazolyls in excited fluorescent (and phosphorescent) states allow the excessive electron-vibrational excitation to be delocalized exclusively on atoms and bonds with similar positions and nature. We will consider practical examples showing that, when excitation corresponding to S* 1 → S0 and T1 → S0 optical transitions and the spectra of pump-induced losses through S* 1 → S* n and T1 → Tn transitions is localized within the bonds of the same type, emission spectra overlap with the spectra of induced losses. This effect gives rise to a strong increase in the threshold pump density. Optical radiation in the ultraviolet range of wavelengths shorter than γmax GEN ≈ 330-320 nm cannot be generated under these conditions directly (without nonlinear frequency conversion). We will perform a comparative analysis of the methods for the investigation of lasing build-up with the use of two-, three-, and five-level models of heteroaromatic azoles as laser active elements.