It is possible to construct fragments of protein structures by using the known values for the fixed bond lengths, bond angles, and torsion angles, and “dialing” in the dihedral angles ϕ and ψ. By choosing these angles in different ways, it is possible to create different populations of fragments and to investigate their properties. We analyzed the following populations: Real fragments taken randomly from known structures. Reconstructed fragments, which are constructed, using the “fixed geometry” assumption, from a set of consecutive pairs of dihedral angles drawn from known structures. Random fragments that are constructed from a random set of dihedral angles from known structures, and doublet‐preserving fragments, which are constructed from a set of dihedral angles drawn at random from known structures in a way such that the distribution of two consecutive pairs of dihedral angles in this population is similar to that distribution in the known structures. We examine the fixed geometry assumption and demonstrate that even reconstructed fragments contain many atomic collisions. We show that random fragments have only slightly more interatomic collisions than the reconstructed fragments. Nevertheless, the population of random fragments is structurally different from the population of reconstructed fragments. On the other hand, we show that the doublet‐preserving fragments exhibit properties that are similar to the real population. Thus the doublet preserving random population can be used to simulate the structure of short polypeptides.