Previous analyses of nutation angle errors from Mark III VLBI data have been made by estimating offset corrections to the instantaneous nutation angles from single-day observing sessions. Adjustments to the coefficients of the nutation model were then estimated from the time series of offset corrections. In this paper we estimate the corrections to the nutation series coefficients directly from the multi-year ensemble of data. The resulting corrections have smaller uncertainties than corrections estimated from the daily offsets because the direct solution has many fewer degrees of freedom. We have forced the corrections to occur at the periods of the dominant terms of the IAU 1980 nutation series instead of allowing the pole orientation to vary freely on each day. Results from daily offset adjustment and direct nutation series adjustment from nearly seven years of data agree at the level of the combined one-sigma uncertainties, 0.1 milliarcseconds. The amplitude of the free core nutation was also estimated from the daily offset data; no significant amplitude was observed.