Recently the Earth System Modelling Group of GeoForschungsZentrum (ESMGFZ) in Potsdam started producing a new series of Effective Angular Momentum Excitation Functions (EAM). As a novelty, the data is given in 3-hour resolution for the influence of the atmosphere and dynamic ocean, and 1-day resolution for terrestrial hydrosphere and barystatic sea-level changes. In addition to this, IERS recently started publishing their new series of C04 solution for Earth Orientation Parameters (EOP), based on new combination of all observations and ITRF2014 terrestrial frame. We use the ESMGFZ data to numerically integrate Brzeziński’s broad-band Liouville equations in celestial frame and compare the results with IERS C04 solution for celestial pole offsets in the interval 1986.0-2018.4. Alternatively, we also add a possible influence of unevenly distributed Geomagnetic jerks (GMJ). In the process of integration we look for the best-fitting parameters (period T, Q-factor) of Free Core Nutation (FCN). It is demonstrated that the fit between integrated and observed values is much better when compared with our previous solutions, based on older models of geophysical excitations. The fit is improved significantly when GMJ quasi-impulse effect is included. The best fit is obtained for atmospheric, oceanic and GMJ excitations, the preferred parameters of FCN being.. . We also estimate new value for empirical prograde MHB Sun-synchronous correction.