The magnetic properties of γ-iron films on Cu(111) below the two-dimensional percolation threshold of about 1.4 monolayer are investigated. Iron on flat Cu(111) surfaces forms triangular patches, while it forms stripes along step edges on vicinal surfaces. The films exhibit an easy magnetization axis perpendicular to the film plane and magnetic hysteresis at sufficiently low temperatures. The magnetization curves of the triangular iron patches are discussed in terms of Ising superparamagnetism. From Kerr hysteresis loops, we deduce that the first anisotropy constant K₁ in the superparamagnetic films is of order 0.345 ± 0.020 MJ/m³.