In his original estimates of the relationship that subsequently became known as the Phillips Curve, Phillips (1958) adopted an unorthodox estimation procedure. This involved replacing the 53 raw observations with six averaged values and then estimating by means of a combination of least squares and graphical inspection. Recently, Desai (1973, 1975) has suggested that Phillips' estimation procedure has interesting economic properties not shared by the orthodox methods used by subsequent workers, and has drawn a distinction between the "Phillips Curve", as estimated by Phillips himself, and the "Lipsey Curve" estimated subsequently. He goes so far as to suggest that the "averaging procedure is a crucial part of Phillips' results and the validity of the original results depend on it" (Desai, 1975, p. 14). The traditional view of Phillips' procedure is that it was a short-cut method to enable the estimation of a nonlinear relationship prior to the widespread availability of modern computing methods (see, e.g., Lipsey, 1960, pp. 3-6). The purpose of this note is to reiterate this view. However, in view of Desai's suggestion, it is necessary to look at Phillips' procedure rather more closely than might otherwise have been necessary, in order to demonstrate precisely why he adopted his obviously inefficient and apparently ad hoc averaging procedure. If we can do this it will follow that Phillips' procedure is only of computational and of neither statistical nor economic interest. It will imply further that there is no distinction between the Phillips Curve and the Lipsey Curve although there may nevertheless be a valid distinction between the Phillips Curve and the "Desai relationship". A byproduct of this study is the re-estimation of the original relationship by modern methods which enable the statistical properties of the relationship to be examined.