Core aeration is the only thing I know of that relieves compaction without destroying the lawn to do it. Tillage and full renovation work, and they kill the grass on the way through. So when soil is genuinely compacted, cores are the correct answer, and I want that on the record, because plenty of people now say aeration does nothing for compaction and that is just as wrong as the flyer calling it a cure.
Two qualifiers, both real. The first is density. Research measures cultivation in cores per square foot, not in passes. K-State puts effective cultivation at 15 to 30 cores per square foot, and a single pass with a commercial spoon aerator delivers roughly half that or less. Two or three passes is what it takes to move the needle. I laid out the core-density numbers and the studies here.
The second qualifier is our dirt. Maury County clay swells and settles and takes its shape back, so holes close in weeks rather than seasons. One pass a year is not a compaction program in this county no matter who sells it to you.
Then there is the piece nobody selling spring aeration brings up: destructive compaction is uncommon in a lawn to begin with. Root channels, soil biology, and freeze-thaw cycling in a Zone 6b to 7a winter work against it year round. Real compaction is nearly always something people did, the same feet or the same tires on the same ground over and over. Most of what gets called compacted soil around here is heavy clay behaving exactly like heavy clay: tight when dry, slow to drain, hard underfoot in August. Cores will not turn that into loam.