A general synthesis approach of aqueous glutathione-capped ternary Ag-In-S, Cu-In-S, and Hg-In-S nanocrystals (NCs) is introduced, allowing the NC composition to be varied in a broad range. Ternary Hg-In-S (HIS) NCs are reported for the first time and found to have the same tetragonal chalcopyrite motif as Cu-In-S and Ag-In-S NCs, corroborated by phonon spectra, while X-ray photoelectron spectroscopic data indicate mercury to be present as Hg+ in the Hg-In-S NCs. Colloidal HIS and Hg-In-S/ZnS NCs showed little or no variations of the spectral width of the photoluminescence band upon NC size selection, temperature variation in a broad range of 10-350 K, deposition of a ZnS shell, or postsynthesis annealing. All these observations are similar to those reported earlier for Ag-In-S and Ag-In-S/ZnS NCs and allowed us to assume a general photoluminescence mechanism for all three ternary compounds, based on the model of radiative self-trapped exciton recombination.