The question has not been solved as to why the Al content in a high-silica zeolite is limited to a specific value. Dempsey’s Al-O-Si-O-Al avoidance rule has been expected to answer this question, complementing Loewenstein’s Al-O-Al avoidance rule. The applicability of Dempsey’s rule to mordenite is investigated experimentally and denied. This is in harmony with Schroder and Sauer’s theoretical results on high-silica faujasites.