An animal trap comprises a complete enclosure with just a small hole in the top wall to provide access to the bait on the inside. The trap is sprung to clamp firmly around an animal's paw only if he reaches down through the hole and lifts the bait. In such case, a trigger arm is raised free of an aligned catch and two thick jaws having no sharp edges are brought quickly together. The initial alignment of the trigger arm may be set precisely by a setting screw, and the threaded engagement with the setting screw prevents misalignment.