We investigated the equilibrium chain-exchange kinetics of amphiphilic diblock copolymer micelles, using a new method based on fluorescence correlation spectroscopy. The micelles were formed from polystyrene-block-poly[oligo(ethylene glycol) methyl ether methacrylate] (PS-POEGMA) in different solvents and studied at various temperatures. This linear-brush copolymer was chosen as a model system, forming micelles with short and bulky corona. Depending on the applied solvent, fast exchange could be observed even at temperatures well below the nominal glass transition of the core-forming PS block. The effect is caused by swelling of the core and allows extensive tuning of the chain-exchange rate by adding to the system minor amounts of good or bad solvent for the core block.