We used isotension-ensemble Monte Carlo simulations to study the properties of brush layers of bottle-brush polymers under lateral compression. The polymers were represented by a freely jointed hard-bead model with one side chain grafted to each bead of the main chain, and we considered variations in side-chain length and bead size. Brush properties, including brush height and surface pressure, were analyzed in the context of a generalized box model. The surface pressure was found to have a steeper dependence on the grafting density than predicted by classical theories of polymer brushes. This discrepancy could be traced to the equation of state of the polymer fluid composing the brush, which was found to be more reminiscent of the concentrated regime than of the semidilute conditions normally expected in polymer brushes. The conformational properties of individual polymer molecules were found to be insensitive to lateral compression; in particular, the side-chain end-to-end distance remained essentially constant.