The GABA(B) (gamma-aminobutyric acid type B) receptor is one of the principal inhibitory neurotransmitter receptors in the brain, and it signals through heterotrimeric G proteins to activate a variety of effectors, including G-protein-coupled inwardly rectifying potassium channels (GIRKs)(1,2). GABA(B)-receptor signalling is tightly regulated by auxiliary subunits called KCTDs, which control the kinetics of GIRK activation and desensitization(3-5). However, the mechanistic basis for KCTD modulation of GABA(B) signalling remains incompletely understood. Here, using a combination of X-ray crystallography, electron microscopy, and functional and biochemical experiments, we reveal the molecular details of KCTD binding to both GABA(B) receptors and G-protein beta gamma subunits. KCTDs associate with the receptor by forming an asymmetric pentameric ring around a region of the receptor carboxy-terminal tail, while a second KCTD domain, H1, engages in a symmetric interaction with five copies of G beta gamma in which the G-protein subunits also interact directly with one another. We further show that KCTD binding to G beta gamma is highly cooperative, defining a model in which KCTD proteins cooperatively strip G proteins from GIRK channels to induce rapid desensitization following receptor activation. These results provide a framework for understanding the molecular basis for the precise temporal control of GABA(B) signalling by KCTD proteins.