A statistical method for the analysis of fluorescence fluctuation amplitudes including bright spikes is presented. This situation arises e. g. when fluorescent ligands interact with receptors carrying multiple binding sites, the technique gives information an the amount of bound ligand in solution, making it a complementary technique to fluorescence correlation spectroscopy analysis, which cannot be applied in this situation. Two simple statistical tests are proposed that can discriminate between fluorescence intensities originating from free ligands or complexes. The performance of the two tests is evaluated and compared on mixtures of a fluorophore and fluorophore-coated beads that mimic the behaviour of multi-liganded complexes. An application to ligand binding to the serotonin receptor, expressed on Escherichia coli cells, is also provided. Specific binding of a fluorophore to this receptor, as well as competition with several ligands, is assessed.