Calculation of third‐order bounds to the conductivity of isotropic two‐component composites is discussed. Coincidence of the Beran bounds and bounds derived using trial fields based on the solution of a single‐body electrostatic boundary‐value problem is demonstrated for a random distribution of impenetrable ellipsoids. This extends a proof of Beasley and Torquato [J. Appl. Phys.60, 3576 (1986)]. A structural parameter related to third‐order bounds is calculated for a face‐centered cubic array of cubes in a matrix. For an array of rectangular blocks an upper bound in one direction is derived. This bound, and its two‐dimensional analogs, become very sharp in the limit of strong inhomogeneity. Improved third‐ and fourth‐order bounds for the three‐dimensional checkerboard are presented.