New flux data are presented for nine non-variable stars and 14 evolved variable stars with spectral types M and C. The data are from measurements of 21 passbands in the wavelength range from 7440{AA} to 10834{AA}, and they are comparable to measurements made by Wing some 40 years ago. Because the extinction algorithm applied to the new data is based partly on up-to-date calculations of telluric water-vapor effects, those calculations are tested for accuracy. In addition, methods used to calibrate standard stars both outside and inside the Paschen confluence are explained. After reddening corrections are applied to the flux data for the variable stars, those data are used to calculate color temperatures. In turn, those temperatures are used to derive blanketing corrections to color temperatures measured in the Wing filter system. Indices of absorption strength are calculated by comparing the flux data to blackbody colors derived from the color temperatures. It is found that the standard errors of those temperatures range from 3% to less than 1%. For the variable stars, the standard errors for the flux data range from 6.8mmag to 11.6mmag. For the non-variable stars, the corresponding standard error is about 6.0mmag.