The noise level in single-pulse resonant nitrogen CARS spectra is shown to decrease with increasing pump laser bandwidth. This is the reverse of the trend observed for nonresonant CARS spectra. The precision of single-pulse CARS temperature measurements is shown to be dramatically increased by performing a weighted fit of theoretical and experimental CARS spectra using the measured detector noise coefficients as weighting parameters. The inclusion of collisional narrowing and cross-coherence in the CARS theory calculations and their effect on best fit temperatures are discussed. These temperatures, measured in a flat-flame burner, are compared with those obtained by Na line-reversal.