  In this paper we try to suggest a possible novel method to determine some
selected even zonal harmonics J_l of the Earth's geopotential. Time series many
years long of suitably linearly combined residuals of some Keplerian orbital
elements of certain existing geodetic SLR satellites would be examined. A
CHAMP/GRACE-only background reference model should be used for the part of the
geopotential which we are not interested in. The retrieved values for the even
zonal harmonics of interest would be, by construction, independent of each
other and of any post-Newtonian features. The so obtained mini-model could,
subsequently, be used in order to enhance the accuracy and the reliability of
some tests of post-Newtonian gravity, with particular emphasis to the
measurement of the Lense-Thirring effect by means of LAGEOS and LAGEOS II.
