The structure and growth of ultrathin Au and Pd films on Cu(001) have been studied by low-energy ion scattering (LEIS) and low-energy electron diffraction (LEED). Due to the existence of a kinetic pathway for intermixing, both Au and Pd are incorporated into the Cu(001) surface at room temperature, forming a surface alloy at a coverage of 0.5 monolayer (ML). At Au coverage near 1.2 ML, the surface layer is pure Au; this is caused by Au-induced segregation from the underlying layer to the surface. No second- and/or third-layer Au is evident. In contrast to this, for the Pd/Cu(001) case a clock reconstruction is formed after deposition of 1 ML Pd. The LEIS data, through comparisons with 3-D computer simulation, reveal a 0.25 Å lateral clockwise - anticlockwise displacement of the first-layer Pd atoms. A simple model for this clock reconstruction is proposed. The driving force behind the dealloying for the Cu - Au alloy and Pd-induced reconstructing for the Cu - Pd surface is also discussed.