Wedging joints adds great strength, but it also is risky. A wedge can split the work, it can fail to dive into the tenon (sometimes popping out of the tenon), or the tenon itself can split when you hit it, making a mess of things.
Here are three things I do to reduce the risk.
1. Make lots of wedges. When I make wedges, I usually make at least 100 so I have lots of them on hand at assembly time. Every wedge is a little different. You might need a thin one for a tight tenon or a big fatty to close up a big gap. I like to make my wedges so they have a 4° included angle at the tip.
2. Add a secondary bevel to the wedge. Right before I drive a wedge home in a tight tenon, I use a knife to carve a quick secondary bevel on both faces of the wedge. This secondary bevel helps start the wedge in tight spaces.
3. If the tenon is still too tight, open it with a chisel. Sometimes even a perfect wedge will fail to open a tight tenon. So I help things along with a chisel. Take a chisel that is the same width as the diameter of your tenon and use it to split the tenon open above the surface of the work. This almost always does the trick.
Last of all, use hide glue. It’s reversible so if you really muck things up, you can apply some heat and moisture, take the joint apart and try again.
— Christopher Schwarz