A height-adjustable implant is designed to be inserted between vertebral bodies and includes a first and a second sleeve part. The second sleeve part carries an external thread and is inserted with a longitudinal section thereof in the first sleeve part in a rotationally fixed and axially movable manner. On its longitudinal section projecting from the first sleeve part, the second sleeve part is encompassed by a nut that engages with the external thread. The nut carries a toothed ring. The invention also relates to a tool for handling the implant.