If standard two-parameter item response functions are employed in the analysis of a test with some newly constructed items, it can be expected that, for some items, the item response function (IRF) will not fit the data well. This lack of fit can also occur when standard IRFs are fitted to personality or psychopathology items. When investigating reasons for misfit, it is helpful to compare item response curves (IRCs) visually to detect outlier items. This is only feasible if the IRF employed is sufficiently flexible to display deviations in shape from the norm. A quasi-parametric IRF that can be made arbitrarily flexible by increasing the number of parameters is proposed for this purpose. To take capitalization on chance into account, the use of Akaike information criterion or Bayesian information criterion goodness of approximation measures is recommended for suggesting the number of parameters to be retained. These measures balance the effect on fit of random error of estimation against systematic error of approximation. Computational aspects are considered and efficacy of the methodology developed is demonstrated.