Tips from a January 2013 thread about patching holes in drywall to accept smaller-diameter recessed fixtures.

I have a homeowner who wants to replace 6" recessed light fixtures with 4" fixtures. Some but not all of the smaller cans will be in the same spots, and I can’t think of a good way to patch a 6" hole and then put a 4" hole in the same spot. — htroberts, North Carolina

Cut out the existing hole to something near a 10"–12" square. Take a piece of 3/8" plywood about 10"?x 20" — adhesive on the ends — prop it up in the hole — pull it down against the back of the existing DW while you put screws up through it from the room side. Put your new hole in —tape and finish. — Happy Home, Greensboro, N.C.

How I repair them (I have repaired many): I cut the mixing sticks for 5-gallon paint buckets in half, place them in the hole, and secure them [with screws]. I have a hole saw for 6" recessed lights, so I cut new slugs out of scrap drywall, place the slug into the hole, and secure to mixing sticks. I tape with FibaFuse (not FibaTape) — it is very thin and lays down really nice — use Easy Sand, then Plus3. That solves the abandoned light locations.

For the locations where you will be putting 4" cans in the same spot: [Create a custom slug from scrap drywall using] a drywall circle cutter, set it to 4" (8" circle), score both sides. On the same center point, reset the cutter to 3" (6" circle), score only the back, then carefully break off the 1" [ring of gypsum] leaving the face paper intact. Using Easy Sand, secure the slug to the ceiling by the [face paper] flange, tape as normal. Bore the hole for new light.

You do know that if there is insulation in the [ceiling], you need IC-rated lights, or keep the insulation 3" from the luminary. I know of no 4" IC recessed luminaries that are a remodel configuration.

One more thing. If you remove the can, you should be able to remove the frame in the ones that get the new luminaries by disassembling the frame through the hole. — tjbnwi, Northwest Indiana