Growth curve models are a useful tool for developmentalists because they can estimate an attribute's developmental function by providing a mathematical description of growth on an attribute over time. However, selection of a growth curve model appropriate for estimating individual developmental functions is problematic. The ideal model is the one that most precisely estimates individual developmental functions from the profile data. But profile data often violate model assumptions. When sample sizes are relatively small, the effects of these violations often are not well understood. For this study, computer simulations were run to identify which types of models provided the most precise descriptions of developmental functions with various types of profile data. Models included: (1) Population Logistic Growth Curve; (2) Population Polynomial Growth Curve; (3) Individual Logistic Growth Curve; (4) Individual Polynomial Growth Curve; and (5) Prototypic Growth Curve. The goals of three analyses were to identify the best model for estimating growth curves when individual differences and reliability are varied, when profile size and reliability are varied, and when more than one parametric family is sampled. All examined data characteristics affected the ability of the models to estimate the profiles. It is concluded that longitudinal studies must be carefully designed if data are to be used to estimate individual growth curves. (RH)