The influence of the tetragonal and orthorhombic axial distortions on the body-centered cubic ͑bcc͒ phase of Fe at extreme conditions has been studied by means of first-principles calculations. We unambigiously demonstrate that the energy minimum corresponding to the body-centered tetragonal ͑bct͒ ͑c / a Ϸ 0.9͒ structure, previously found in Fe upon the axial tetragonal distortion of the bcc phase along the Bain's path under compression at zero temperature, is an artifact of the structural constraint. When the bcc structure is examined using the orthorhombic distortion involving the tetragonal distortion as a particular case, the bct ͑c / a Ϸ 0.9͒ structural framework represents a saddle point between two mirrored face-centered cubic minima rather than a local minimum. Therefore we conclude that there is no ground to emphasize on possible thermal stabilization of the bct structure with a particular c / a ratio apart from the whole family of structures obtained by tetragonal, orthorhombic, or another type of axial distortions.