Strontium titanate single crystals 15-20 mm in diameter and 40-80 mm in length were grown by a floating zone method with radiation heating. Additional crystal heating just below the molten zone by an in-growth annealing furnace was applied in order to lower the temperature gradients and to achieve slower cooling of the grown crystal. The crystal perfection was studied with X-ray topography and double-crystal diffractometry. The most perfect crystals were grown in [0 0 1] direction with single grain rocking curve widths of about 30" and subgrain misorientations of 1'-3' over 10 x 10 mm(2) areas of the boule cross-section for both (0 0 1)-, (1 1 0)- and (1 1 1)-oriented slices. Such high-quality crystal can be grown reproducibly with starting materials of 4N grade quality. (C) 2002 Elsevier Science B.V. All rights reserved.