In this work, we studied how an amphipathic peptide of the surface of the globular protein thioredoxin, TRX94-108, acquires a native-like structure when it becomes involved in an apolar interaction network. We designed peptide variants where the tendency to form alpha-helical conformation is modulated by replacing each of the leucine amino acid residues by an alanine. The induction of structure caused by sodium dodecyl sulfate (SDS) binding was studied by capillary zone electrophoresis, circular dichroism, DOSY-NMR, and molecular dynamics simulations (MDS). In addition, we analyzed the strength of the interaction between a C18 RP-HPLC matrix and the peptides. The results presented here reveal that (a) critical elements in the sequence of the wild-type peptide stabilize a SDS/peptide supramolecular cluster; (b) the hydrophobic nature of the interaction between SDS molecules and the peptide constrains the ensemble of conformations; (c) nonspecific apolar surfaces are sufficient to stabilize peptide secondary structure. Remarkably, MDS shed light on a contact network formed by a limited number of SDS molecules that serves as a structural scaffold preserving the helical conformation of this module. This mechanism might prevail when a peptide with low helical propensity is involved in structure consolidation. We suggest that folding of peptides sharing this feature does not require a preformed tightly-packed protein core. Thus, the formation of specific tertiary interactions would be the consequence of peptide folding and not its cause. In this scenario, folding might be thought of as a process that includes unspecific rounds of structure stabilization guiding the protein to the native state.