What is needed for high-level radioactive waste is not necessarily a program for final disposal, but rather an early clear demonstration that an acceptable method is available. This would be especially easy for ocean dumping, since the environment in the water just above the ocean floor is much more uniform, stable, predictable, and more easily reproduced in a laboratory than other environments being considered for waste storage. Other probable advantages of ocean dumping are improved capability for monitoring and retrievability and reduced cost and transport problems. It is assumed that the waste is incorporated into glass and dumped in oceans distributed throughout the world. Calculations of environmental impacts are given for various assumptions about leach rates and failures and for a 30 000-yr delay in onset of leaching achieved by surrounding the waste with a protective coating. With normal leaching, there would be 0.17 eventual human fatalities per GW(electric)-yr, and for the worst case of immediate complete dissolution, this is increased by only 30%. This is 150 times less than the fatalities due to wastes from coal-fired plants. Calculations of effects on ocean ecology are based on 105 GW(electric)-yr (100 yr with all the world’s power nuclear). Under essentially all reasonably credible conditions, the radiation dose to marine life is never as high as 1% of their exposure from natural radiation (0.1%) for microbiota). Evidence is presented that this would do essentially no harm to ocean ecology.