On October 12, 2002, approximately 1255 mountain daylight time, a Mooney M20K, N231EH, impacted a fence during the landing roll at Madison County Airport, Rexburg, Idaho. The private pilot and his three passengers were not injured, but the aircraft, which is owned and operated by Air Bound, LLC., sustained substantial damage. The 14 CFR Part 91 personal pleasure flight, which departed Driggs, Idaho, about 55 minutes earlier, was being operated in visual meteorological conditions. No flight plan had been filed. According to the pilot, he entered a left downwind for Runway 17 with the intention of making a full stop landing on the 4,200 foot strip. He reportedly touched down on the runway numbers, but inadvertently allowed the aircraft to balloon back into the air. After a few seconds, the aircraft touched down a second time, but then ballooned even higher. According to the pilot, when the aircraft touched down the third time, he "...added some power to stay on the ground." This resulted in the aircraft lifting off the runway for a third time. After the aircraft settled on the surface for the fourth and final time, the pilot concluded that he would not be able to stop before reaching the fence located just off the south end of the runway. At that point he decided to add full power in an attempt to clear the fence and complete the landing roll in the area beyond it. Although he got the aircraft off the ground, the landing gear caught on the fence and pulled the aircraft to the ground. Soon thereafter, the left wing collided with a tree and the aircraft came to rest. According to the pilot, there was no evidence of any malfunction of the flight control system or the engine. He also stated that during the entire landing sequence, including during the time he attempted to "clear the fence," the wing flaps were in the fully deployed (down) position. In his narrative report, he also stated that he has now learned to execute a go-around if the wheels are not firmly planted by the time the aircraft reaches the second VASI (Visual Approach Slope Indicator).