A method of applying dry and substantially thermal and acoustical insulation by spraying an air entrained stream of high velocity pils into cavities, including vertical wall cavities, without having to use any insulation securing means is disclosed. A nozzle system is used that comprises a shredder section for reducing the size of the pieces of insulation to pil size and an accelerator section for increasing the velocity of a stream of air suspended pils for improved just-installed insulation integrity or strength.