We have observed HD 101177B and 149414A, two known single-lined binaries, and directly measured the radial velocities of their secondaries, enabling us to derive the mass ratios of the two systems. Using high signal-to-noise ratio spectra obtained mostly with the William Herschel Telescope, and a new algorithm to analyse composite spectra, TODCOR, we show that the mass ratios of HD 101177B and 149414A are 0.48+/-0.03 and 0.57+/-0.02, respectively. These are two of the lowest mass ratios ever measured around normal G or K dwarf stars. These two systems demonstrate the potential of the present approach, which can turn many of the known single-lined binaries into double-lined systems. Such work has important implications for the study of the mass-ratio distribution of many samples of binaries.