As many as 20% of adults at some point suffer from a painful digestive disorder that is difficult to diagnose and has no cure. Treatment is hit or miss, and many sufferers never seek help because they find the symptoms hard to discuss.

Irritable bowel syndrome (IBS) has long baffled gastro-intestinal experts. Some think it is caused by imbalances in gut bacteria; others point to psychological stress. Now, a small but growing contingent of specialists is focusing on food intolerances as a possible culprit—and a new dietary...