A process for making a closed-cell, alkenyl aromatic polymer foam structure having enlarged cell size. An alkenyl aromatic polymer material is heated to form a melt polymer material. An amount of a non-waxy cell size enlarging agent is incorporated into the melt polymer material. The enlarging agent is present in an amount sufficient to enlarge the stabilized cell size of the formed foam structure by 20 percent or more over a corresponding foam structure made without the enlarging agent. Further, the enlarging agent is incorporated in a quantity such that the formed foam structure has physical properties substantially the same degree as the corresponding foam structure. A blowing agent is incorporated into the melt polymer material at an elevated pressure to form a foamable gel. The foamable gel is expanded in a zone of lower pressure to form the foam structure. Further, disclosed is a foam structure corresponding to the above.