Methods and devices for reducing the mineral content of a region of non-intimal vascular tissue are provided. In the subject methods, an isolated local environment that includes the region to be demineralized is produced. The pH of the local environment is then reduced to a subphysiologic level, e.g. by flushing with an acidic dissolution fluid, for a period of time sufficient for the mineral content of the region to be reduced. The devices of the subject invention are characterized by comprising a means for producing an isolated local environment that includes a non-intimal region of vascular tissue. Also provided are kits for practicing the subject methods.