Thermally deposited ultrathin Fe films on Cu(111) at room temperature or below have been known to grow in a multilayer mode with a low net magnetic moment (  ∼  0.5μ_B). In the present work we have used pulsed laser deposition to produce isotropic fcc Fe/Cu(111) films which grow layer by layer with a magnetic moment of more than 2μ_B. We attribute the larger magnetic moment of the pulsed laser deposited films to their structural perfection as seen by low energy electron diffraction and scanning tunneling microscopy.