The stretcher is what gives a trestle table its stability. The way it attaches to the leg is interesting: A tenon fits through a mortise in the leg, but then there is a mortise in the tenon to house a wedge. The wedge tightens the joint but can be removed if the table needs to be disassembled.
The mortise in the tenon can be tricky. I started with a 1″ thick stretcher. The resulting tenon was 3/4″ thick, so the wedge was quite narrow – only 3/8″. It works, but I definitely wouldn’t go any narrower. If I were to start over, I would pick 5/4″ material for the stretcher.
The stretcher tenon is relatively long and I only wanted to worry about the fit where the legs meet the tenon’s cheek. The remainder of the tenon is tapered on all sides so it passes through the mortise easily.
The result is pleasing: a tight fitting wedge. I am using walnut as a complimentary material to the mahogany for joinery. The dowels for the legs and breadboard ends are made of walnut, too.
T r i a l & E r r o r 
That looks fantastic!
I’ve learned the hard way that the tenon that extends past the wedge needs to be long for a good reason. When you drive the wedge, if the tenon doesn’t have enough meat behind the wedge, the short grain there will bust out and you get to make a new stretcher.
Yeah – that brings back bad memories from a previous project, too!