Nozzles for converting clumps and nodules of dry or substantially dry fibrous insulation to pils and for spraying on the so treated and accelerated air entrained insulation pieces to form thermal and acoustical insulation in building cavities. The nozzles comprise a shredder section for reducing the size of many 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. The shredder and the accelerator can also be combined in a single unit.