If you’re using knife/chisel/router plane, don’t be afraid to go back with the knife to cut through the grain so your chisel is less likely to tear things out. And if you get some small tear-out, you can always glue the bit back in place, wait for the glue to dry (I generally wait overnight, because at that point I need a mental break, even if I’m still ok physically), and come back later for a second try.
A LOT of my shop furniture will have small repairs like that, because I find it’s the most effective way of teaching myself to do things correctly, and I mostly practice new techniques on shop furniture.