Using computer simulation of a coarse-grained, bead-spring model as well as scanning-probe microscopy of polytBA brushes in ethanol, we demonstrate that upon compression a poor solvent between two apposing polymer brushes does not remain a uniform thin film but, instead, forms a lateral, nanoscopic structure. The characteristic lateral length scale of the solvent domains scales with the brush height that, in turn, can be controlled by the grafting density, molecular weight, or pressure. These findings are rationalized in terms of geometric considerations, accounting for the interfacial free energy between the solvent and the brush and the spatial arrangement of the grafted chains. The phenomenon offers a general strategy to laterally structure confined fluids.