The spectral bandwidth formulae of Stearns and Stearns (Color Res Appl 1988; 13: 257-259) are generalized for an arbitrary slit function. Correction coefficients are derived in terms of moments of the slit function. Application to model LED spectra measured with a compact, fiber-coupled spectrometer having bandwidth of order 12 nm, and a nonlinear wavelength scale shows that accurate LED color measurements may be obtained with such an instrument. Fitting of the relatively broad slit function to line spectra for accurate wavelength calibration is also described. Such fitting, coupled consistently with the bandpass correction, improves the accuracy color measurements with a broad-response spectrometer. (C) 2006 Wiley Periodicals, Inc.