A method and apparatus for making an optical fiber preform. The apparatus has an outer wall and an inner wall. The outer wall surrounds the inner wall and the inner wall surrounds an inner cavity of the apparatus. A core rod is deposited in the inner cavity after which particulate glass material, such as glass soot, is deposited in the inner cavity around the core rod. The core rod has at least 10 percent of the final cladding soot already applied thereto. A radially inward pressure is applied against the particulate glass material to pressurize the particulate glass material against the core rod.