Here we report the observation of a highly non-linear bubble response of phospholipid coated contrast agents, termed 'compression-only behavior' where the microbubbles only compress, yet hardly expand. The occurrence of this phenomenon has been studied retrospectively and it was found that 33% of the examined cases show this behavior. The compression-only behavior is described by a newly developed shell model for phospholipid coated bubbles. The model extends previous elastic models with shell compressibility, a buckling radius and a break-up tension. It also predicts large amplitude oscillations, and bubble break-up.