Help with lock rabbet joints

[Kellyn Kusyk]

Hey y’all—I’m building a cherry chest (approx 5’ long, 20” high & 20” deep) with solid panels for each side. The joints connecting the sides to the front/back are lock rabbets, running the entire height of the side panels. However when dry fitting the panels together just now I realized I have a gap of about 1/32” within the lock rabbet joint—see photos attached. That means I don’t have any friction in the joint while dry fitting. Will glue in this joint be sufficient to close the gap and make a strong, durable joint? I’m considering pinning the joint with a dowel, but the dado/tenon piece is 1/2” thick, meaning the dowel would only be able to be about 1/4”—is this thick enough of a dowel to strengthen the joint significantly?487649487650

[Cameron Wood]

Add a strip of veneer?

[Lee Schierer]

Add a strip of veneer?

Or a shaving from a hand plane.

[Dwayne Watt]

The gap is no where near 1/32", but could stand to be a little tighter. Shimming with appropriate thickness material off your table saw would work. Brown paper bag material would also work. Keep in mind that this joint should not be "tight" when dry fit. The material adjacent to the dado groove is weak and likely to be broken if there is any semblance of interference in the joint.