Evolutionary algorithms (EAs) have been with us for several decades and are highly popular given that they have proved competitive in the face of challenging problems’ features such as deceptiveness, multiple local optima, among other characteristics. However, it is necessary to define multiple hyper-parameter values to have a working EA, which is a drawback for many practitioners. In the case of genetic programming (GP), an EA for the evolution of models and programs, hyper-parameter optimization has been extensively studied only recently. This work builds on recent findings and explores the hyper-parameter space of a specific GP system called neat-GP that controls model size. This is conducted using two large sets of symbolic regression benchmark problems to evaluate system performance, while hyper-parameter optimization is carried out using three variants of the iterated F-Race algorithm, for the first time applied to GP. From all the automatic parametrizations produced by optimization process, several findings are drawn. Automatic parametrizations do not outperform the manual configuration in many cases, and overall, the differences are not substantial in terms of testing error. Moreover, finding parametrizations that produce highly accurate models that are also compact is not trivially done, at least if the hyper-parameter optimization process (F-Race) is only guided by predictive error. This work is intended to foster more research and scrutiny of hyper-parameters in EAs, in general, and GP, in particular.