Bacteria commonly live in dense and genetically diverse communities associated with surfaces. In these communities, competition for resources and space is intense, and yet we understand little of how this affects the spread of antibiotic-resistant strains. Here, we study interactions between antibiotic-resistant and susceptible strains using in vitro competition experiments in the opportunistic pathogen Pseudomonas aeruginosa and in silico simulations. Selection for intracellular resistance to streptomycin is very strong in colonies, such that resistance is favoured at very low antibiotic doses. In contrast, selection for extracellular resistance to carbenicillin is weak in colonies, and high doses of antibiotic are required to select for resistance. Manipulating the density and spatial structure of colonies reveals that this difference is partly explained by the fact that the local degradation of carbenicillin by β-lactamase-secreting cells protects neighbouring sensitive cells from carbenicillin. In addition, we discover a second unexpected effect: the inducible elongation of cells in response to carbenicillin allows sensitive cells to better compete for the rapidly growing colony edge. These combined effects mean that antibiotic treatment can select against antibiotic-resistant strains, raising the possibility of treatment regimes that suppress sensitive strains while limiting the rise of antibiotic resistance. We argue that the detailed study of bacterial interactions will be fundamental to understanding and overcoming antibiotic resistance.