Just a thought from experiencing a baby with frequent hiccups myself. My little daughter later started having problems with gas that was painful at times. We suspected something in my wife's diet was causing excess gas so we kept a database of what my wife ate along with when the daughter's gas problems ensued. We found out that broccoli was the culprit. Apparently, cruciferous veggies (cabbage family) like broccoli, cauliflower, cabbage and such were putting substances into mother's milk that caused excess gas in the baby. My wife stopped eating these veggies and the excess gas problems stopped. I wonder if avoiding those veggies would stop the hiccuping in your precious baby? I looked online and hiccups in babies do seem to be related to gas in the digestive tract. Even though the hiccups are harmless it still almost hurts to watch a baby with them. And congratulations, BTW!