The growth and ordering of a Pb layer deposited on Cu(001) at 150 K has been studied using atom beam scattering. At low coverage, ordered Pb islands with (61 × 61) R tan-1 (5/6) symmetry are formed. This is a high-order commensurate phase with 30 atoms in the unit cell. From the measurement of the island diffraction peak profiles we find a power law for the mean island size versus coverage with an exponent n=0.54±0.03. A scaling behavior of growth is confirmed and a simple model describing island growth is presented. Due to the high degeneracy of the monolayer phase, different islands typically diffract incoherently. Therefore, when islands merge they still diffract as separate islands and coalescence effects are thus suppressed. From the result for n we conclude that the island density is approximately a constant in the coverage range 0.1<FTHETA<0.5 where the ordered islands are observed [FTHETA is defined as the ratio between the number of Pb atoms and the number of Cu atoms in the underlying Cu(001) layer]. We thus conclude that most islands nucleate at FTHETA<0.1 and then grow in an approximately self-similar fashion as FTHETA increases.