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Morphology changes and irreversible reorientation of the easy magnetization axis upon annealing of thin epitaxial fcc-iron films grown at 100 K on Cu(100) were studied in situ with scanning tunneling microscopy and the magneto-optical Kerr effect. An irreversible spin reorientation from in-plane to out-of-plane is observed for 6 monolayers thick iron films annealed to 350 K. This change in magnetic anisotropy is accompanied by considerable smoothing of the iron film surface. Annealing to higher temperatures leads to a strong increase of the coercive field by up to a factor of 6. The surfaces of these films are atomically flat and display some scattered needle-like protrusions and dislocation lines.