In the search for a correlation between the magnetism and the microstructure of ultrathin films, straightforward layer-by-layer growth is desirable. The thermal deposition of Fe onto Cu(111), however, does not result in this growth mode. In this letter, we compare the initial growth of Fe on Cu(111) prepared by pulsed laser deposition (PLD) with thermally deposited Fe/Cu(111) using scanning tunneling microscopy (STM). In PLD, from the beginning there is two-dimensional nucleation and growth, in contrast to the initial bilayer nucleation and growth found for thermal deposition. Therefore, it is shown by STM that PLD grown films exhibit greatly improved layer-by-layer growth. The different experimental results are interpreted in terms of the very high deposition rate during PLD.