A blood-drawing device has a specimen tube having a projecting tip having an outer connection region of a predetermined diameter and a guide sleeve fittable over the tip and having an inner resilient part. The inner resilient part has an inside diameter smaller than the diameter of the connection region. A needle fitted to the guide sleeve is surrounded by an elastomeric tubular needle shield inward from the guide sleeve. The sleeve can move between an outer position with the needle shield extending inward past the inner needle end and the resilient part offset outward from the connection region and an inner position with the needle end in the specimen tube, the needle shield compressed between the sleeve and the specimen tube, and the resilient part fitting tightly around the connection region and deformed outwardly thereby such that the resilient part grips the connection region.