I got a piece of mail from my Credit Union with some tips on saving fuel. One was to avoid running on empty. "When your car is on empty, you're actually using more gas because your vehicle is running less efficiently. Fill your gas tank when you have about a half tank." (Credit Union of NJ, June 2007). I've never heard of this, so I checked the internet and found a few mentions of this.
I don't get how having more fuel on board makes your car run more efficiently.