First-principles theoretical investigations of one-dimensional ordered 3d-5d alloys reveal magnetic anisotropy energies E, which are extraordinary high for transition-metal nanostructures. The results show that ∆E of Pt-X and Ir-X wires with X ≡ Ti-Ni strongly oscillates as a function 3d-band filling showing both giant values (e.g., ∆E = 25, 58, and 57 meV/atom for Pt-Ni, Ir-Cr, and Ir-Ni) as well as modest enhancements (e.g., ∆E = 2.3 and 6.5 meV/atom for Pt-Cr and Pt-Fe). The robustness of the results with respect to strain and relaxation is demonstrated. The microscopic mechanisms behind the trends in ∆E are analyzed from a local perspective.