In order to assess the accuracy of a recently adjusted relativistic energy-consistent small-core pseudopotential for uranium, the U5+ (5f(1) subconfiguration) spin-orbit splitting as well as the fine structure of the U4+ (5f(2) subconfiguration) spectrum have been calculated. The pseudopotential has been adjusted to four-component all-electron data, i.e., at the multiconfiguration Dirac-Hartree-Fock level using the Dirac-Coulomb Hamiltonian with a Fermi nucleus charge distribution and perturbatively including the Breit interaction. Its performance in a dressed effective Hamiltonian spin-orbit configuration interaction framework is compared to that of an older scalar-relativistic Wood-Boring adjusted pseudopotential, supplemented by a valence spin-orbit term, as well as to all-electron calculations using the Douglas-Kroll-Hess Hamiltonian. Electron correlation is accounted for by the multireference configuration interaction method with and without the Davidson correction and with different frozen-orbital spaces. Our best calculations show satisfactory agreement with experimental data; i.e., the mean absolute (relative) deviations amount to 183 (2.4%) and 948 cm(-1) (5.1%) for the U5+ and the U4+ fine-structure energy levels, respectively. Even better agreement, comparable to the one for rigorous highly correlated four-component all-electron data, is obtained in intermediate Hamiltonian Fock-space coupled-cluster calculations applying the new pseudopotential.