Protein folding cooperativity is defined by the nature of the finite-size thermodynamic transition exhibited upon folding: two-state transitions show a free energy barrier between the folded and unfolded ensembles, while downhill folding is barrierless. A microcanonical analysis, where the energy is the natural variable, has shown better suited to unambiguously characterize the nature of the transition compared to its canonical counterpart. Replica exchange molecular dynamics simulations of a high resolution coarse-grained model allow for the accurate evaluation of the density of states, in order to extract precise thermodynamic information, and measure its impact on structural features. The method is applied to three helical peptides: a short helix shows sharp features of a two-state folder, while a longer helix and a three-helix bundle exhibit downhill and two-state transitions, respectively. Extending the results of lattice simulations and theoretical models, we find that it is the interplay between secondary structure and the loss of non-native tertiary contacts which determines the nature of the transition. ; Comment: 3 pages, 3 figures