I second what Pat B said. I have never, well rarely had a problem with Titebond III and every time I can attribute it to my own mistakes.
If the surfaces are prepped (i'd personally sand them lightly with 120 grit or something near there). And the fit is tight ... and I mean tight. Then you are good to go.
If you're using Titebond, when you clamp everything up, I leave the excess glue along the glue line where it squeezes out. I never wipe it away. While the glue is drying, if there is a very tiny gap, it will draw some of that excess glue back in.