Groundwater model parameters need to be inferred on the basis of limited observation data, resulting in prediction uncertainty. The reduction of this uncertainty via future complementary observations is of high importance for many problems and can be guided by Bayesian experimental design. We employ a novel combination of Bayesian inversion, accelerated via multilevel methods, and Bayesian experimental design for this purpose. For a synthetic aquifer, we analyze the effect of including or excluding environmental tracer observations besides groundwater heads in two scenarios. In both scenarios, we study the effect of available data on distributions of model predictions after Bayesian inversion and subsequent experimental design. We demonstrate that posterior samples from Bayesian inversion can be reused to perform experimental design without additional model evaluations. In both scenarios, uncertainties and biases of flux-related and groundwater age-related predictions are substantially reduced through experimental design. Compared to the scenario with groundwater heads alone, including environmental tracer data in the observation data set leads to less uncertainty and bias in model outputs after Bayesian inversion, greater reduction of uncertainty and bias through experimental design, and reduced overestimation of complementary observation worth. Including environmental tracer observations at the beginning of combined Bayesian inversion and experimental design leads to more reliable predictions and more effective future data acquisition.