Two algorithms of decomposition of composite protein tryptophan fluorescence spectra were developed based on the possibility that the shape of elementary spectral component could be accurately described by a uniparametric log-normal function. The need for several mathematically different algorithms is dictated by the fact that decomposition of spectra into widely overlapping smooth components is a typical incorrect problem. Only the coincidence of components obtained with various algorithms can guarantee correctness and reliability of results. In this paper we propose the following algorithms of decomposition: (1) the SImple fitting procedure using the root-Mean-Square criterion (SIMS) operating with either individual emission spectra or sets of spectra measured with various quencher concentrations; and (2) the pseudo-graphic analytical procedure using a PHase plane in coordinates of normalized emission intensities at various wavelengths (wavenumbers) and REsolving sets of spectra measured with various Quencher concentrations (PHREQ). The actual experimental noise precludes decomposition of protein spectra into more than three components.