This invention is an electrosurgical instrument (10) for sequentially cutting and coagulating tissue, including methodology for electrosurgical procedures incorporating principles of the inventive instrument. The instrument comprises a cutting electrode (18) connectable to a first power source (22b) having a first power signal sufficient to cut tissue, and a coagulating electrode (20) connectable to a second power (22a) source having a second power signal sufficient to coagulate tissue. The electrodes may be separated by an electrical insulator (36) to maintain the electrodes in a spaced relationship such that the coagulating electrode can immediately follow the cutting electrode during movement of the instrument, thereby providing sequential cutting and coagulating of tissue. Methods for providing an electrosurgical procedure include providing the instrument with power delivery to the electrodes. The cutting electrode receives a power signal sufficient to cut tissue and the coagulating electrode receives a power signal sufficient to coagulate tissue. The distal ends of the electrodes are introduced to tissue and moved therethrough with a single stroke to thereby cut tissue followed by simultaneous coagulation. The electrodes may be formed of differing cross section configurations, and may be vertically offset to maximize cutting and coagulation of tissue. An in-dwelling dispersible electrode (100) may be utilized to concentrate electrosurgical energy at a desired tissue site.