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A close comparison between the segregation data obtained by means of DFT-based calculations and diffusion experiments is provided using the grain boundary (GB) segregation of Ag, Au, Se, Ge, Ni, Co and Bi impurities in Cu as a case study. The density functional theory calculations along with the McLean segregation isotherm are applied to obtain the effective segregation energies of the solute atoms to a representative special GB in Cu. GB diffusion measurements in both B- and C-type kinetic regimes in the same polycrystalline high-purity Cu are used to access the segregation behavior of solutes in the true dilute limit. In the case of Ag and Bi, a very close comparison is possible as the experiments have been conducted on ideal Cu bi-crystals with a GB where we find an excellent agreement between theory and experiment. For the other solutes, the DFT data for the GB are used to mimic behavior of general high-angle interfaces. For Bi, Se, and Ge, the experimental picture is consisted with the DFT results, while for Ni, Co and Au, serious discrepancies are found. The reasons for the discrepancies are analyzed and discussed in the paper. In addition, we investigate the influence of the selected impurities on the mechanical strength of the GB in the framework of the Rice-Thompson-Wang theory and identified the most harmful elements from the point of view of the cohesive destrengthening of the interface.