Objects are fastened to a support with a variety of staples or tacks (14a or 14b or 14c or 14d or 14e) using a hand-held appliance (1) that comprises a tubular element (17), designed to accommodate a bonded strip (36) of the staples or tacks (14a...e) purchased as a refill, a guide bar (18) positioned internally of the tubular element (17) along which the refill strip (36) is slidable, a spring-loaded element (27) by which the strip (36) is pushed in the direction of a restraining plate (30) located at one end of the tubular element (17), and a punch rod (7) by which the staples or tacks are separated singly from the strip and driven downwards, sliding against the surface of the plate (30); the top part of the guide bar (18) is chased with a longitudinal and vertically disposed groove (21), whilst the restraining plate (30) affords one or more slots or grooves (32 or 33a, 33b) in which to seat at least one leaf spring (33' or 33a, 33b) extending toward the longitudinal groove (21), or lower, and serving to maintain the correct position of the staple or tack as the rod (7) descends.