The traditional mesoscopic paradigm represents DNA as a series of base-pair steps whose energy response to equilibrium perturbations is elastic, with harmonic oscillations (defining local stiffness) around a single equilibrium conformation. In addition, base sequence effects are often analysed as a succession of independent XpY base-pair steps (i.e. a nearest-neighbour (NN) model with only 10 unique cases). Unfortunately, recent massive simulations carried out by the ABC consortium suggest that the real picture of DNA flexibility may be much more complex. The paradigm of DNA flexibility therefore needs to be revisited. In this article, we explore in detail one of the most obvious violations of the elastic NN model of flexibility: the bimodal distributions of some helical parameters. We perform here an in-depth statistical analysis of a very large set of MD trajectories and also of experimental structures, which lead to very solid evidence of bimodality. We then suggest ways to improve mesoscopic models to account for this deviation from the elastic regime.