We analyzed six years of very–long–baseline interferometry (VLBI) data and determined corrections to the coefficients of the seven terms with the largest amplitudes in the IAU 1980 nutation series. Our analysis yields results consistent with earlier analyses of smaller sets of VLBI data, within the uncertainties of the latter. Here, we restrict discussion to the freely excited core–nutation or “free core–nutation” (FCN). Our analysis yields an estimate of 0.33 ± 0.12 mas for an assumed constant amplitude of the FCN, which allows us to place an upper bound on it of 0.6 mas (99.5% confidence limit). We also studied possible temporal variations of the complex amplitude of the FCN by modeling it as a stochastic process with a white noise excitation. We detected no statistically significant variations of this amplitude for the six–year interval spanned by the VLBI data. However, in the neighborhood of one cycle per day, the power spectral density of the atmospheric surface loading is estimated from global weather data to be 0.24 (g cm−2)2 day, about five times larger than the largest such power spectral density that would be consistent with the upper bound on the amplitude of the FCN placed by the VLBI data. Thus, we conclude that this estimate is too high and that, if the FCN were excited by surface loads with frequencies near one cycle per day, then the power spectral density of these loads must be <0.06 (g cm−2)2 day (99.9% confidence limit).