A syringe (20) is disclosed including a needle (22) and a barrel (24). The needle can have an outside surface (32), a delivery outlet (34) at one end, a base (36) at the other end, and an internal passage (38) extending from the base to the delivery outlet. The barrel can have a generally cylindrical interior surface portion (40) defining a lumen. The barrel also can have a front passage (44) molded around and in fluid-sealing contact with the outside surface of the needle. A method of making such a syringe is also disclosed. A mold (80) for making the barrel defines a front opening of the barrel to be molded around and in fluid-sealing contact with the outside surface of the needle. The needle is positioned within the mold cavity, with its base abutting the core. The barrel is molded against the needle to join the barrel and the needle.