Soft x-ray linear and circular dichroism (XLD, XMCD) experiments at the Ce M4,5 edges are being used to determine the energy scales characterizing the Ce 4f degrees of freedom in the ultrathin ordered surface intermetallic CeAgx/Ag(111). We find that all relevant interactions, i. e. Kondo scattering, crystal field splitting and magnetic exchange coupling occur on small scales. Our study demonstrates the usefulness of combining x-ray absorption experiments probing linear and circular dichroism owing to their strong sensitivity for anisotropies in both charge distribution and paramagnetic response, respectively.Rare earth intermetallic compounds display a rich phenomenology of physical properties, encompassing very different kinds of ground states, such as magnetic order, unconventional superconductivity and paramagnetic heavy fermion liquids [1,2]. The interaction of localized 4f electrons with itinerant electronic degrees of freedom may result in the emergence of small characteristic energy scales which produce nontrivial macroscopic behavior at low temperature and complex phase diagrams with competing interactions and orders [1][2][3][4][5]. In a solid environment, the degeneracy of the rare earth 4f ground configuration is lifted by the crystal field in general, causing both an anisotropic 4f charge distribution and, in conjunction with spin orbit coupling, (single ion) magnetic anisotropy. Unraveling the crystal field induced level structure thus constitutes an essential part of understanding the low temperature physics and of establishing correlations between local 4f symmetry at low temperature on the one hand and macroscopic ground state properties on the other.In this respect, the usefulness of probing the 4f configuration with linear polarized soft x-rays [6] has been demonstrated for a variety of Ce compounds in recent years [7][8][9][10][11][12][13][14], allowing to settle several open issues, where other experiments left room for diverging interpretations. Its magnetic variants, x-ray magnetic linear and circular dichroism (XMLD, XMCD) constitute sensitive element and orbital specific probes of magnetic polarization and anisotropy [15][16][17][18][19][20]. XMCD was successfully utilized to reveal the presence of magnetic Kondo screening in CePt 5 /Pt(111) [21].In the present letter we demonstrate that the combined use of linear and magnetic circular dichroism allows us to determine the crystal field structure without recourse to e. g. inelastic neutron scattering, as in some previous work [7][8][9]. Our chosen example of an ultrathin Ce-Ag surface intermetallic furthermore highlights a threefold advantage of this approach. First, linear and circular dichroism experiments are frequently both feasible with the same installation and therefore can be performed in situ within a single experimental run. Second, the splittings turn out to be of the order of 1 meV only, making their discrimination from quasi-elastic scattering a difficult task. Last but not least, the sample volume is so small that most alter...