Abstract: Electromedical apparatus is employed together with local topically applied drugs and general medical management program to non-invasively, non-traumatically, reduce in volume without fat cell death, specific local accumulations of stored triacylglyceride by localizing (e.g., focusing) radiant energy and/or localized lipolysis augmentation methods, thereby accelerating local fat tissue lipolysis reaction rates. The radiant energy includes, localized radio frequency, microwave or ultrasound energy, which impinges upon the fat cells to be reduced in volume but not killed or eliminated. Fat cell size reduction occurs through the mechanism of accelerated lipolysis rate which is a function of local cell temperature elevation and local fat cell lipolysis rate augmentation by local lipolytic drug delivery.