Sensitivity spectra of Stark-shift voltage sensitive dyes, such as ANNINE-6, suggest the use of the extreme red edges of the excitation spectrum to achieve large fractional fluorescence changes with membrane voltage. This was tested in cultured HEK293 cells. Cells were illuminated with light at the very red edge of the dye's excitation spectrum, where the absorption cross section is as much as 100 times smaller than at its peak. The small-signal fractional fluorescence changes were -0.17%/mV, -0.28%/mV, and -0.35%/mV for one-photon excitation at 458 nm, 488 nm, and 514 nm, respectively, and -0.29%/mV, -0.43%/mV, and -0.52%/mV for two-photon excitation at 960 nm, 1000 nm, and 1040 nm, respectively. For large voltage swings the fluorescence changes became nonlinear, reaching 50% and -28% for 100 mV hyper- and depolarization, respectively, at 514 nm and 70% and -40% at 1040 nm. Such fractional sensitivities are approximately 5 times larger than what is commonly found with other voltage-sensing dyes and approach the theoretical limit given by the spectral Boltzmann tail.