Helices are among the predominant secondary structures in globular proteins. About 90% of the residues in them are found to be in the alpha -helical conformation, and another 10% in the 3(10) conformation. There is a standing controversy between experimental and some theoretical results, and controversy among theoretical results concerning the predominance of each conformation, in particular, helices, We address this controversy by ab initio Hartree-Fock and density functional theory studies of helices with different lengths in a vacuum and in the aqueous phase. Our results show that (1) in a vacuum, all oligo(Ala) helices of 4-10 residues adopt the 3(10) - conformation; (2) in aqueous solution, the 6-10 residue peptides adopt the alpha -helical conformation; (3) there might be two intermediates between these helical conformers allowing for their interconversion. The relevance of these results to the structure and folding of proteins is discussed.