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We consider the problem of setting approximate confidence intervals for a single parameter theta in a multiparameter family. The standard approximate intervals based on maximum likelihood theory, can be quite misleading so, in practice, tricks based on transformations, bias, corrections, etc., are often used to improve their accuracy. The bootstrap confidence intervals discussed in this paper automatically incorporate such tricks without requiring the statistician to think them through for each new application, at the price of a considerable increase in computational effort. In addition to parametric families, bootstrap intervals are also developed for nonparametric situations. Originator-supplied keywords include: nonparametric intervals and Secondary order theory., Sponsored in part by Grants NSF-MCS80-24649 and N00014-83-G-0121.