The molecular arrangement of 4,4′-biphenyldicarboxylic acid (BDA) on Cu(001) has been studied at high coverage and relatively high temperature (∼400 K) using Low Energy Electron Microscopy, LEEM, and selected area diffraction, μLEED. Next to the previously reported c(8 × 8) structure, we also observe a compressed phase with a superstructure in matrix notation. All four equivalent (rotational and mirror) domains are equally populated. Both the c(8 × 8) and the compressed phase are confined to the first layer and the latter has a 14% higher density compared to the c(8 × 8) phase. Remarkably, this compressed phase is stable only during deposition and decays after interruption of the deposition. Apparently, the density of physisorbed admolecules on top of the c(8 × 8) layer has to be above a relevant threshold to allow the formation of the compressed phase.