Artificial linear regressions often provide a convenient way to calculate test statistics and estimated covariance matrices. This paper discusses one family of these regressions, called "double-length" because the number of "observations" in the artificial regression is twice the actual number of observations. These double-length regressions can be useful in a wide variety of situations. They are quite easy to calculate, and seem to have good properties when applied to samples of modest size. We first discuss how they are related to the more familiar Gauss-Newton and squared-residuals regressions for nonlinear regression models, then show how they may be used to test for functional form, and finally discuss several other ways in which they may be useful in applied econometric work.