Ni/Cu(100) films are known to exhibit an "inverse" reorientation transition. In contrast to Fe or Co ultrathin films one observes that the magnetization rotates from in plane to out of plane upon increasing the thickness. The driving force of this phenomenon is a bulk uniaxial anisotropy due to the tetragonal film structure, which favors an out-of-plane orientation. On the other hand, Fe/Cu(100) films grown at 80 K display a reorientation from out-of-plane to in-plane when the thickness is increased. The question arises how the different thickness dependencies evolve upon alloying. We find that the reorientation equivalent to Ni/Cu(100) is displayed only at Fe contents below 8%, which can be explained within a magnetoelastic model. In the interval 35-75% Fe we find a reorientation transition equivalent to Fe/Cu(100). Further increase of the Fe content leads to "magnetic live surface layers" whose appearance is correlated to structural changes as seen by low-energy electron diffraction.