Low-dimensional parametric models are well understood, straightforward to communicate to other workers, have very smooth curves and may easily be checked for consistency with background scienti"c knowledge or understanding. They should therefore be ideal tools with which to represent smooth relationships between a continuous predictor and an outcome variable in medicine and epidemiology. Unfortunately, a seriously restricted set of such models is used routinely in practical data analysis } typically, linear, quadratic or occasionally cubic polynomials, or sometimes a power or logarithmic transformation of a covariate. Since their #exibility is limited, it is not surprising that the "t of such models is often poor. Royston and Altman's recent work on fractional polynomials has extended the range of available functions. It is clearly crucial that the chosen "nal model "ts the data well. Achieving a good "t with minimal restriction on the functional form has been the motivation behind the major recent research e!ort on non-parametric curve-"tting techniques. Here I propose that one such model, a (possibly over-"tted) cubic smoothing spline, may be used to de"ne a suitable reference curve against which the "t of a parametric model may be checked. I suggest a signi"cance test for the purpose and examine its type I error and power in a small simulation study. Several families of parametric models, including some with sigmoid curves, are considered. Their suitability in "tting regression relationships found in several real data sets is investigated. With all the example data sets, a simple parametric model can be found which "ts the data approximately as well as a cubic smoothing spline, but without the latter's tendency towards artefacts in the "tted curve.