Using computer simulations as a tool for thought experiments, we investigate the influence of the helical backbone geometry in the association process and the final structures of a simple model which mimics parallel, two-stranded coiled-coil proteins. We define three types of helices: two of them have straight helical axes and 3.5 or 3.6 residues per helical turn; the third type presents a coiled helical axis, according to the canonical scheme defined by Crick. By using a Monte Carlo simulation algorithm, we observe that the three models exhibit different transition temperatures for the formation of the dimeric structure from two independent peptides, and a different behavior concerning the appearance of out-of-register structures. The energy minimized dimer structures present strong deviations from the correct association for straight helices with 3.6 residues/turn, especially for long peptides, deviations which are absent for the other two types when only the burial of hydrophobic residues is considered. A careful analysis of the energies for the out-of-register configurations and the contact maps reveals also differences between dimers resulting from the model with Crick parameterization and with 3.5 residues/turn. The results presented in this paper may be relevant for the design of simple models which use rigid alpha-helices built from predicted elements of secondary structures.