The structural and morphological changes of a 1.1 monolayer (ML) Pt deposit on W(1 1 1) have been investigated in situ, in ultra-high vacuum, as a function of the annealing temperature from 700 to 1340 K, by a combination of grazing incidence X-ray diffraction and grazing incidence small-angle X-ray scattering. Before annealing, the thin Pt layer is two-dimensional and lattice-matched to the W(1 1 1) surface. The faceting of Pt/W(1 1 1) towards nanoscale three-sided pyramids with {2 1 1} facets has been detected from 715 K. At this stage, the pyramids, which have a 5-nm average lateral size, cover nearly perfectly the surface. At higher temperatures, they increase in size. The role of the edge energy in the nanofaceting process is discussed. In addition, 4 MLs Co are deposited at room temperature on the smallest Pt/W pyramids. The obtained three-dimensional Co islands are correlated with the Pt/W nanopyramids and Co is relaxed on Pt/W. At approximately 800 K, a CoPt alloy is formed and becomes better ordered as the annealing temperature increases. At 1100 K, both defaceting and phase separation begin; the CoPt alloy segregates on the W(1 1 1) flat surface, while Co forms an epitaxial layer on the {2 1 1} facets. In addition, in the temperature range of 1100–1200 K, a great majority of {2 1 1} large facets coexist with some {1 1 0} small facets. Finally, the surface becomes flat again at 1250 K.