This invention relates to a method of preparing a brominated elastomer having a stabilized Mooney viscosity. The method includes polymerizing isomonoolefins and at least one polymerizable unit to obtain an elastomer/polymer; brominating the elastomer/polymer to form a brominated elastomer effluent; neutralizing the brominated elastomer effluent to form a neutralized effluent; volatizing off the hydrocarbon solvent; and recovering a brominated elastomer. In at least one point of the process, preferably prior to any significant temperature change in the brominated polymer, a Mooney stabilizer is added into the system. Portions of the Mooney stabilizer may be added at multiple points into the process.