Context. The International Astronomical Union (IAU) adopted a new precession model at its 2006 General Assembly. After more than ten years since the publication of the so-called IAU 2006 precession, we have noticed progress in solar system ephemerides and geophysical observations, which can be used to refine the precession model. Another progress is the increase by 30% since 2003, of the length of the very long baseline interferometry (VLBI) observations to be compared with the theoretical model. Results. For the precession of the ecliptic, the changes in the new solutions with respect to the IAU 2006 are about several tens of microarcseconds in the linear terms of P A and Q A . The upgraded precession of the equator is such that the quadratic and cubic terms in the quantity ψ A differ significantly from IAU 2006 due to the revised J 2 model. The statistics of the VLBI celestial pole offsets and least squares fits with different empirical models, show that the LC precession is slightly more consistent with the VLBI observations, but the improvement relative to the IAU 2006 model is not definitely convincing at present. Conclusions. The upgraded LC precession obtained with the latest theoretical and observational improvements has shown some advantages with respect to the IAU 2006 model. However, due to negligible changes in the precession of the ecliptic and large uncertainties in the J 2 variation, we recommend that the standard IAU 2006 model be retained for practical use and continuity reason. The next precession-nutation model should be constructed with a uniform dynamical approach in the framework of ICRF3 and Gaia reference frame and without the use of a conventional ecliptic.