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Dislocation structure and slip plane are two key elements to understanding the basic mechanism of plastic deformation in metal alloys. Using density-functional theory (DFT), we investigate the influence of Ta and Re on the non-planar 12〈111〉 screw dislocation in body-centered cubic W. The dislocation-core structure is modeled by the dislocation–dipole approach, and the effect of alloying is determined from the virtual-crystal approximation as well as the supercell method. Both reveal symmetric core structures for W–Ta alloys but asymmetric ones for W–Re. Our ab initio results allow for an evaluation of the inter-row model, which is found to produce dislocation-core structures consistent with DFT results, but fails to describe the dislocation movement in these alloys. DFT finds the slip plane to be altered by Re alloying. This result is confirmed by microcantilever bending tests.