The effect of the interplay between surface tension and gravity on the sedimentation of objects in structured fluids is investigated by simulating the quasi-static motion of a spherical particle through an ordered foam. We describe the path which a sphere takes as it descends through bamboo (1,1,0), staircase (2,1,1), chiral (3,2,1), and double staircase (4,2,2) foams, and measure the degree of control of the sphere’s motion that each foam offers. For an ordered foam contained within a vertical cylinder, the resulting sphere motion depends strongly on the structure itself, on how the films are deformed near the sphere, and on how the motion of the sphere deforms them further. For staircase and chiral foams, the distance that a sphere is pulled away from the center-line of the cylinder by the foam is found to depend on the Bond number with a power-law relation. By tilting the cylinder at an angle to the vertical, we show that there exists a critical tilt angle above which the sphere falls out of the foam. This angle is dependent on the choice of foam structure and the Bond number. For a sphere of given size and given Bond number in the ordered foams studied here, the greatest tilt can be imposed on the double staircase foam.