The response of stimuli-responsive polymer brushes to moderately elevated pressure is investigated by neutron reflectivity and a thermodynamically consistent density functional theory where pressure effects are included by a hydrophobic cavity model. Evidence is provided that temperature and pressure effects on the brush spatial structure are entirely antagonistic. A similar to 100 bar/K cancellation effect is found, which we argue is a general feature for hydrophobically associating homopolymers and serves for experimental guidance and fine-control of polymer film structure. Our results also suggest that polymeric interfaces which do not show a marked temperature dependence are also rather insensitive to pressure effects for applied pressures below 1 kbar.