Using the South Pole Acoustic Test Setup (SPATS) and a retrievable transmitter deployed in holes drilled for the IceCube experiment, we have measured the attenuation of acoustic signals by South Pole ice at depths between 190 m and 500 m. Three data sets, using different acoustic sources, have been analyzed and give consistent results. The method with the smallest systematic uncertainties yields an amplitude attenuation coefficient alpha = 3.20 +/- 0.57 km(-1) between 10 and 30 kHz, considerably larger than previous theoretical estimates. Expressed as an attenuation length, the analyses give a consistent result for lambda equivalent to 1/alpha of similar to 300 m with 20% uncertainty. No significant depth or frequency dependence has been found. (C) 2010 Elsevier B.V. All rights reserved.