A computational approach has been developed to assess the power of paramagnetism-based backbone constraints with respect to the determination of the tertiary structure, once the secondary structure elements are known. This is part of the general assessment of paramagnetism-based constraints which are known to be relevant when used in conjunction with all classical constraints. The paramagnetism-based constraints here investigated are the pseudocontact shifts, the residual dipolar couplings due to self-orientation of the metalloprotein in high magnetic fields, and the cross correlation between dipolar relaxation and Curie relaxation. The relative constraints are generated by back-calculation from a known structure. The elements of secondary structure are supposed to be obtained from chemical shift index. The problem of the reciprocal orientation of the helices is addressed. It is shown that the correct fold can be obtained depending on the length of the alpha-helical stretches with respect to the length of the non helical segments connecting the alpha-helices. For example, the correct fold is straightforwardly obtained for the four-helix bundle protein cytochrome b562, while the double EF-hand motif of calbindin D9k is hardly obtained without ambiguity. In cases like calbindin D9k, the availability of datasets from different metal ions is helpful, whereas less important is the location of the metal ion with respect to the secondary structure elements.