Won’t say that I speak with any authority on the subject; but being at best an acceptably mediocre woodworker, there is some gathered experience on it.
If the mating(?) piece hasn’t shoulders, it might be of value to create at least one. Then glue a strip/shim along the created tenon. Finally plane the strip until the piece fits the housing.
If the piece going into the housing is to match something else – another housing, as in a shelf, for instance – then experience has taught me the importance of making sure along which face I make the groove.
My alternative approach is to shim the housing enough to allow a minute rebate/shoulder on the mating piece, shouldn’t there be a pair in beforehand (which there, as a precaution always are). I use wedged strips to press the shims to the side of the housings, and then wait for the glue to cure. Some masking tape on the strips saves them from getting stuck in the dado.
The attached photos show the contraption used for sliding dovetails. Please accept my apologies on them potentially being a tad artistic. For square dadoes I use strips wedged along their length.
The nice thing is that the shoulders hide the shims.
London, UK; Boston, MA