Since your first pass goes all the way through to the tail, you actually will get more meat. Try it you'll like it. When cleaning fish take that extra time to prepare it properly. Remember to remove all blood line from fish that have this dark red meat. It is most often found parallel with the spine.
Some fish have lots others have none.
When present it will pay dividends if you take the time to remove the blood line before cooking. Some people are fanatics about salvaging every shred of meat. I am specifically talking about removing all bones or blood line when cleaning. I couldn't enjoy eating it, and that is the ultimate goal when cleaning fish. When cleaning fish many people, myself included, often use electric fillet' knives.