Binding along the beam axis (which we shall call "longitudinal optical binding") has been observed between micron-sized oil droplets in a three dimensional optical trap in air. We argue that it is the high optical contrast which is responsible for the exceptionally stable doublet structures observed experimentally. It was also observed that optically bound doublets tend to cling to interference fringes created by the two counterpropagating beams. Our observations are qualitatively discussed in the context of both the ray model (optics) approximation, and in the Rayleigh (dipolar) range. Our observations were consistent with calculations of binding and trapping forces which we carried out by employing an exact multiple-scattering theory.