An electrosurgical instrument is provided for cauterization and/or welding of tissue of varying impedances, thicknesses and vascularity especially in the performance of endoscopic procedures. The instrument compresses the tissue between an electrode associated with a first pole of a bipolar energy source located on one interfacing surface off a first element, and a second interfacing surface of a second element. The first and second elements are used to engage and compress tissue between the first and second interfacing surfaces. A second electrode associated with a second pole is located one of the two interfacing surfaces. The first electrode is either recessed into the first tissue contacting surface and/or offset from the second electrode on the same or opposing surfaces. A preferred application of the invention is in a cutting instrument wherein a hemostatic line is formed along a cut line using RF energy.