A method is provided for modulating the rate of release of a therapeutic agent from a release region, which constitutes at least a portion of an implantable or insertable medical device and which controls the rate at which the therapeutic is released from the medical device. The method comprises: (a) providing a release region that comprises (i) a therapeutic agent and (ii) polymer composition comprising two or more immiscible phases; and (b) modulating the rate of release of the therapeutic agent by changing the volume that is occupied by at least one of the immiscible polymer phases relative to the total volume of the release region that is formed. The release region can be, for example, a carrier layer, which comprises the therapeutic agent, or a barrier layer, which is disposed over a region that contains the therapeutic agent. In preferred embodiments, the release region is formed by a process comprising: (a) providing a solution comprising (i) a solvent and (ii) the polymer composition; and (b) forming the release region from the solution by removing the solvent from the solution.