A clamping device having a pair of jaws that mounts on to an object and utilizes a fulcrum and leveraging mechanism to provide a combination of leveraged force and compression force to improve clamping and withstand vibration. This configuration provides enhanced gripping action at the open end of the jaws, which is especially advantageous when mounted near the edge of an object, such as a shelf. The clamping device can be low profile, compact and lightweight. The interior sides of the parallel jaws of the clamping device can be padded to prevent damage. This clamping device enables fastening to an accessory support for supporting the weight of items that extend beyond a center of gravity of the device. These items can include audio or video cables extending beyond shelves of on an audio equipment rack, or lighting and grip equipment, or can be used in any industry or endeavor.