That's the secret. The closer you get to the middle, the better the joint will look, otherwise you'll have to sand, sand, sand, sand, sand to even it up. Get Terrie Noll's "Joint Book" for the last word on all kinds of joints. I'll be using lap joints to make stage scenery flats, and hitting the half way point precisely is important when you have from 6 to 8 joints per flat. You don't want to do much hand work. Glue on a lap joint will make it almost impossible to break.
A video I saw a couple of years ago had the builder cutting to the half way mark with a Japanese pull saw, and using that line to guide the router. Flats are made of soft pine so he just plows through, but with hard woods, you'd want to take off layers.
I saw a recent post that showed a very large mortising bit that was just for this kind of flattening, but I can't find it just now.
The more I do, the less I accomplish.