Protein coats deform flat lipid membranes into buds and capture membrane proteins to form transport vesicles. The assembly/disassembly cycle of the COPI coat on Golgi membranes is coupled to the GTP/GDP cycle of the small G protein Arf1. At the heart of this coupling is the specific interaction of membrane-bound Arf1-GTP with coatomer, a complex of seven proteins that forms the building unit of the COPI coat. Although COPI coat disassembly requires the catalysis of GTP hydrolysis in Arf1 by a specific GTPase-activating protein (ArfGAP1), the precise timing of this reaction during COPI vesicle formation is not known. Using time-resolved assays for COPI dynamics on liposomes of controlled size, we show that the rate of ArfGAP1-catalysed GTP hydrolysis in Arf1 and the rate of COPI disassembly increase over two orders of magnitude as the curvature of the lipid bilayer increases and approaches that of a typical transport vesicle. This leads to a model for COPI dynamics in which GTP hydrolysis in Arf1 is organized temporally and spatially according to the changes in lipid packing induced by the coat.