First-principles theoretical calculations of the core-level binding-energy shift ͑CLS͒ for eight binary facecentered-cubic ͑fcc͒ disordered alloys, CuPd, AgPd, CuNi, NiPd, CuAu, PdAu, CuPt, and NiPt, are carried out within density-functional theory ͑DFT͒ using the coherent potential approximation. The shifts of the Cu and Ni 2p 3/2 , Ag and Pd 3d 5/2 , and Pt and Au 4f 7/2 core levels are calculated according to the complete screening picture, which includes both initial-state ͑core-electron energy eigenvalue͒ and final-state ͑core-hole screening͒ effects in the same scheme. The results are compared with available experimental data, and the agreement is shown to be good. The CLSs are analyzed in terms of initial-and final-state effects. We also compare the complete screening picture with the CLS obtained by the transition-state method, and find very good agreement between these two alternative approaches for the calculations within the DFT. In addition the sensitivity of the CLS to relativistic and magnetic effects is studied.