Asbtract:  Smooth curve fitting can be carried out as a stand-alone exercise, or for the effect of individual covariates within linear models. Penalty function methods for doing this lead to a spline-type formulation, and the 'most common' method for choosing the penalty coefficient, as in journal citations, is cross-validation. Because cross-validation uses a criterion different from those in a penalty function formulation, and different again from indicators of consequent unwanted bias in linear models, there are a number of inter-related, potentially confusing questions about how these models should be set up and fitted. Following an intuitive non-parametric approach leads to a Cramer-von Mises method which may settle some of these questions, as well as leading to a surprising alternative formulation.