The current regulation of biological invasions rests on an unwarranted presumption (that the invader will cause no harm) and on risk assessment procedures that are narrowly focused, subjective, often arbitrary and unquantified, and subject to political interference. Although this current approach dominates international treaties and most national policies, it has not stemmed the rising tide of biological invasions, as evidenced by several examples from the USA. Technical advances in measuring and predicting impacts of introduced species will improve risk assessments. Additionally, focusing squarely on the risks associated not only with a proposed species introduction, but also on the goals of the introduction and on alternative ways of achieving them, would lead to more-informed decisions permitting the introduction of a species and fewer problematic invaders. In assessing the alternatives to introductions, the precautionary principle should be given heavy weight, as should the distribution of possible costs and benefits.