A nose assembly for pulling fasteners through a workpiece includes an anvil having a conical surface for engaging a complimentary conical surface defined by a set of chuck jaws. The chuck jaws includes a rear skirted portion defining a recess for receiving a biased support member which prevents the radial collapse of the chuck jaws during actuation of the nose assembly. The nose assembly is particularly adapted for gripping a relatively short axially projecting portion of a fastener while ensuring complete engagement of all jaw teeth with the fastener.