Relatively mild annealing sometimes produces unexpectedly large changes in surface composition of ultra-thin films. We report results of a scanning tunnelling microscopy study of such annealing in an Fe/Cu(100) system. Copper appears in the surface region after a short 490 K anneal. We specifically exclude the possibility of bulk interdiffusion and conclude that this surface copper comes from the substrate through microscopic pinholes. Our primary finding is that the balance of surface free energies which strongly prefers Cu/Fe/Cu over Fe/Cu is the main driving force for pinhole formation and copper segregation. Furthermore, we report a significant surface alloying in this otherwise almost immiscible system.