The enhancement of stimulated Raman scattering (SRS) of weak-gain Raman modes in pendant drops is accomplished by overlapping Stokes wavelengths of the Raman modes with the Rhodamine 640 dye-lasing gain region (called the gain-overlap method). The dye concentration and the pumping intensity of frequencydoubled Nd: YAG lasers determine the efficiency of the enhancement. We apply the gain-overlap technique at optimal dye concentration and pump intensity to probe minority species in pendant drops formed by binary mixtures. The limits of detectable concentrations of the minority species, methanol in methanol-ethanol and ethanol in ethanol-water (dye-doped) mixtures, are much less than those in undoped mixtures. The smooth fluorescence-lasing spectral curves emitted from dye-doped pendant drops reduce complications in distinguishing SRS signals from quasi-periodic fluorescence-lasing spectra in microdroplets.