Despite the lack of a rigorous theory that would allow one to construct them in a systematic way, a potentially useful pragmatic solution within the Dirac-Coulomb-Breit framework has been known for a long time. Since relativistic effects become important at high densities -that is, in exchange-dominated core regions -one could, in a first approximation, restrict oneself to an appropriate treatment of the exchange energy. For the exchange energy of the relativistic homogeneous electron gas (RHEG) , a multiplicative correction (a kind of "enhancement factor") has been derived as a simple analytic function Φ(β ), where β = (3π 2 ρ) 1/3 /c (in atomic units). This function satisfies Φ(β ) > 1 and tends to one at the low-density limit; it is a sum of both Coulomb (longitudinal) and Breit (transverse) contributions. This scheme has been implemented and tested for atoms at the LDA level 110 and subsequently extended to the GGA level 111 via data on the linear response of the RHEG to a weak perturbing potential. Data for several small diatomics are available as well. While valence-shell related properties turned out not to be sensitive with respect to these corrections, 112 a high sensitivity of core one-electron energies of heavy atoms has been clearly demonstrated. For heavy atoms, these corrections seem to be of the same order of magnitude as atomic (nonrelativistic) correlation energies. So far, it appears that these corrections have not yet been implemented into a molecular or solid-state code. Obviously, studies of the impact on core-related properties will be of interest. Recently, short-range LDA and GGA exchange functionals have been developed and implemented in a similar way, but again only for atoms and ions so far.