New interventional methods and devices for reducing gastric volume, and thereby treating obesity, are disclosed. The procedures are generally performed laparoscopically and may generally be described as laparoscopic plication gastroplasty (LPG) in which, after obtaining abdominal access, spaced apart sites on a gastric wall are engaged and approximated to create one or more tissue folds that are then secured by placing one or more tissue fasteners to produce one or more plications projecting into the gastrointestinal space. These procedures are preferably carried out entirely extragastrically (i.e. without penetrating through the gastrointestinal wall), thereby minimizing the risks of serious complications. Minimally invasive devices for engaging, approximating and fastening soft tissues are disclosed that enable these new interventional methods to be carried out safely, efficiently and quickly.