Experimentally and computationally, the structure of Pt-Cu at 1:3 stoichiometry has a convoluted history. The L13 structure has been predicted to occur in binary alloy systems, but has not been linked to experimental observations. Using a combination of electron diffraction, synchrotron X-ray powder diffraction, and Monte Carlo simulations, we demonstrate that it is present in the Cu-Pt system at 1:3 stoichiometry. We also find that the 4-atom, fcc superstructure L13 is equivalent to the large 32-atom orthorhombic superstructure reported in older literature, resolving much of the confusion surrounding this composition. Quantitative Rietveld analysis of the X-ray data and qualitative trends in the electron-diffraction patterns reveal that the secondary X1+(a,0,0) order parameter of the L13 phase is unexpectedly weak relative to the primary L1+(a,a,0,0) order parameter, resulting in a partially-ordered L1 3 ordering, which we conclude to be the result of kinetic limitations. Monte Carlo simulations confirm the formation of a large cubic superstructure at high temperatures, and its eventual transformation to the L13 structure at lower temperature, but also provide evidence of other transitional orderings.