Fluorescence lifetime of hypersensitive 4f-4f transitions of rare-earth elements embedded in amorphous inorganic solids can be dramatically modified by compositional adjustment of the hosts tantamount to not more than 1 mol % without any elaborated thermal treatments. It is possible to modify a spontaneous emission rate of Dy3+:(F-6(11/2),H-6(9/2))->H-6(15/2) transition in chalcogenide Ge-As-S glasses through selective addition of low levels of Ga and CsBr. Along with the change of the spontaneous emission rate, multiphonon relaxation rate involved in the (F-6(11/2),H-6(9/2)) state also significantly varies upon the minute compositional adjustment. The combination of these effects results in the measured lifetime of the fluorescing (F-6(11/2),H-6(9/2)) level being greatly enhanced. Such behaviors are attributed to the hypersensitive nature associated with the H-6(15/2)<->F-6(11/2) transition and preferential coordination of bromine in the nearest-neighboring shell of the Dy3+ ions, which is formed spontaneously during the vitrification process of the host materials. These experimental observations show the most extreme dependence of the fluorescence lifetime on small compositional changes reported compared to any other noncrystalline solid-state dielectric. As such coutilization of many hypersensitive transitions of rare-earth elements and those host materials used in this study may present a unique opportunity to control absorption and emission properties, especially fluorescence lifetimes, through a minute compositional adjustment.