Method and apparatus for electrosurgery including tissue coagulation using very high voltage pulses of electrical energy applied to the electrosurgical probe. This minimizes heating of the surrounding tissue in the probe and is especially suitable for precise and limited coagulation and fulguration without excessive tissue charring or other damage. The power at rated load of the applied pulses to the probe is typically over 300W and the duration of the on time is very short, so each group of pulse bursts is of relatively low duty cycle. An RF generator is also provided for delivering electrical energy to an electrosurgical probe with the proper characteristics, including fast switching times.