This invention identifies important geometric parameters of an adhesive microfiber with mushroom-shaped tip for improving and optimizing adhesive ability. The magnitude of pull-off stress is dependent on a wedge angle γ and the ratio of the tip radius to the stalk radius β of the mushroom-shaped fiber. Pull-off stress is also found to depend on a dimensionless parameter x, the ratio of the fiber radius to a length-scale related to the dominance of adhesive stress. Finally, the shape of edge tip, where the surface and sides of the mushroom-shaped tip join, is a factor that impacts strength of adhesion. Optimizing ranges for these parameters are identified.