I have found building in can lights to be not too big a chore. I use 5/8" drywall (already fire-rated). 2 pieces cut to fit the joist space, 1 piece cut to fit across the top of the joists to give a fair amount of captured air space (in case it is an old fixture), a couple drywall clips for the in-joist pieces (same as you would use for doing drywall in a hi-po framing corner), a handfull of drywall screws, fire-rated foam-in-a-can. Real quick, real tight. Too late for this blog, but you might be real disappointed in how leaky ICAT can lights are, even after sealing the can to the ceiling.
This is very good info, however this wall now needs a fire delay covering (usually drywall). If the basement will not be used as a finished space, you can use Thermax brand foam panels as this has the fire delay layer built-in.
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