Should editors of scientific journals practice triple-anonymous reviewing? I consider two arguments in favor. The first says that insofar as editors’ decisions are affected by information they would not have had under triple-anonymous review, an injustice is committed against certain authors. I show that even well-meaning editors would commit this wrong and I endorse this argument. The second argument says that insofar as editors’ decisions are affected by information they would not have had under triple-anonymous review, it will negatively affect the quality of published papers. I distinguish between two kinds of biases that an editor might have. I show that one of them has a positive effect on quality and the other a negative one, and that the combined effect could be either positive or negative. Thus I do not endorse the second argument in general. However, I do endorse this argument for certain fields, for which I argue that the positive effect does not apply.