This is the most obvious, but botched jobs can dampen even the best insulation.
Installation is key. Whether hard foam, sprayed foam, fiberglass/rock wool, or blown-in fiberglass/cellulose, the insulation should fill ceilings, floors, and walls entirely without compressing itself. There should be no gaps.
Also, make sure the "R-value" -- the insulation's resistance to heat flow -- is as high as possible.
Jonathan Wiggs/Globe Staff