The structure and dynamics of polymer brushes have been the subject of considerable theoretical and experimental activity. Experimental measurements of the steric forces between grafted brushes and the structure of a single brush at the solid-solution interface are in good agreement with theoretical predictions. Yet, the structure that brush layers adopt during compression has remained elusive. We report experimental density distribution measurements of two polymer brushes as a function of compression. We find a significant increase in brush concentration at the interface as the layers are compressed in contrast to the smoothly increasing concentration that has been predicted. The interpenetration of the brushes has also been determined. These results demonstrate that high-density brushes collapse under confinement and explain why polymer brushes under good solvent conditions are so effective in decreasing the friction between surfaces.