An improved safety hypodermic syringe includes a reciprocal tubular needle sheath disposed on the exterior of the syringe body, a latch mechanism engaging the syringe body and the sheath to latch the sheath in a needle-covering position after delivering contents from the syringe body, and a spring engaging the syringe body and the sheath and expandable to move the sheath to cover the needle point, where the spring is a non-uniform helical spring having multiple 360° turns each turn uniformly spaced from adjacent turns, each 360° turn comprising first and second alternating angled portions, the first of the alternating angled portions being at a first angle to a plane perpendicular to an axis through the center of the helical spring and the second angled portions being at a second lesser angle to the plane perpendicular to the axis.