Binary adhesive packings of microspheres with certain size ratios are investigated via a 3-D discrete-element method specially developed with adhesive contact mechanics. We found a novel phenomenon that the packing fraction of the binary adhesive mixtures decreases monotonically with the increase of the amount of small components. It was further divulged that this behavior results from the competition between a geometrical filling effect and an adhesion effect. The positive geometrical filling effect only depends on the size ratio, while a dimensionless adhesion parameter Ad is used to characterize the negative adhesion effect, which comes to its maximum at Ad approximate to 10. Structural properties, including contact network, partial coordination number, radial distribution function, and angular distribution function, are analyzed to give a better understanding of such adhesive binary packings. (c) 2017 American Institute of Chemical Engineers AIChE J, 63: 4296-4306, 2017