We analyzed high-resolution spectra of interstellar C I absorption toward λ Ori, 1 Sco, and δ Sco that were obtained with the Goddard High Resolution Spectrograph on the Hubble Space Telescope. Several multiplets were detected within the wavelength interval 1150-1200 Å, where most C I lines have illdefined oscillator strength; multiplets at longer wavelengths with well-defined atomic parameters were also seen. We extracted accurate column densities and Doppler parameters from lines with precise laboratory-based f-values. These column densities and b-values were used to obtain a self-consistent set of f-values for all the observed C I lines. For many of the lines with wavelengths below 1200 Å, the derived f-values differ appreciably from the values quoted in the compilation by Morton. The present set of f-values extends, and in some cases supersedes, those given by Zsargó, Federman, & Cardelli, which were based on lower resolution data.