A spin-reorientation transition upon a variation of the Fe concentration x is observed in ultrathin fcc Fe_xCo_{1− x} alloy films on Cu(001) for x > 77% . For film thicknesses below 4 monolayers the magnetic easy axis changes from in-plane on the Co-rich side to out-of-plane on the Fe-rich side. Since no structural transitions accompany this spin-reorientation transition, varying the alloy composition can be interpreted as varying the number of 3d electrons. Upon changing the average d-band filling by as little as 0.1 electron strong changes of the anisotropy energy are observed.