Coarse-graining or model reduction of dynamical systems is a modelling tool used to extend the time-scale of simulations in a range of fields. When applied in molecular dynamics with moderate time-scale separations, standard coarse-graining approaches seek to approximate the potential of mean force, and use this to drive an effective model. Meanwhile, there is no free lunch: fewer degrees of freedom necessarily means lower accuracy of the resulting model. Here, I will discuss work with Dr Thomas Hudson from the University of Warwick, UK, in which we derived a hierarchy of models to coarse-grain simple systems and analysed the resulting models. It is shown that while the standard recipe for model reduction accurately captures equilibrium statistics, it is possible to derive an easy-to-implement Markovian effective model to better capture dynamical statistics such as the mean-squared displacement. Our results focus particularly on the temporal accuracy of coarse-grained models. Both analytical and numerical evidence for the efficacy of the new approach is provided.