A numerical analysis is presented of cell adhesion in capillaries whose diameter is comparable to or smaller than that of the cell. In contrast to a large number of previous efforts on leukocyte and tumor cell rolling, much is still unknown about cell motion in capillaries. The solid and fluid mechanics of a cell in flow was coupled with a slip bond model of ligand-receptor interactions. When the size of a capillary was reduced, the cell always transitioned to "bullet-like" motion, with a consequent decrease in the velocity of the cell. A state diagram was obtained for various values of capillary diameter and receptor density. We found that bullet motion enables firm adhesion of a cell to the capillary wall even for a weak ligand-receptor binding. We also quantified effects of various parameters, including the dissociation rate constant, the spring constant, and the reactive compliance on the characteristics of cell motion. Our results suggest that even under the interaction between P-selectin glycoprotein ligand-1 (PSGL-1) and P-selectin, which is mainly responsible for leukocyte rolling, a cell is able to show firm adhesion in a small capillary. These findings may help in understanding such phenomena as leukocyte plugging and cancer metastasis.