Known zeolite structures have relatively few 7-membered rings. Previous quantum mechanical calculations suggest there is no particular energy penalty for 7-membered rings. Predicted zeolite structures sampled from all possible symmetries also do not explain why there are so few observed 7-membered rings. Here, we analyze the ring size distributions of predicted structures as a function of energy and density. We show that predicted structures with low density, in the range where known zeolites exist, have relatively few 7-membered rings. It appears that the constraint of proximity to the low-density edge of predicted structures is what leads to a low probability of 7-membered rings. These results suggest that low-density predicted structures are similar to known zeolites and of greatest interest as new synthetic targets.