A power screwdriver (10) includes a bit holder (14) bored to receive the shaft of a screwdriver bit (12) and adapted to securely hold the screwdriver bit (12) in place, and a housing (18) having a through cavity (16). The bit holder (14) is inserted into the through cavity (16) so that the bit holder (14) is rotatable about and movable along the axis of the bit holder. This arrangement securely holds the screwdriver bit and thus, minimize rattling of the screwdriver bit during rotation.