Height of your lawn

I set my deck for 4.5, which I think is really about 3.5. This is a new yard for me and it's mostly Bermuda. I've always cut taller to hold in the moisture and hopefully crowd out the weeds, but this is my first Bermuda. When I moved here I thought it was all crab grass! (I have a little of that, too) Should we taylor our cutting height to the type of grass, or just stick with the one third rule and our own personal preferences?