The common characteristics of amyloid and amyloid-like fibrils from disease- and non-disease-associated proteins offer the prospect that well-defined model systems can be used to systematically dissect the driving forces of amyloid formation. We recently reported the de novo designed ccβ peptide model system that forms a native-like coiled-coil structure at low temperatures and which can be switched to amyloid-like fibrils by increasing the temperature. Here, we report a detailed molecular description of the system in its fibrillar state by characterizing the ccβ-Met variant using several microscopic techniques, circular dichroism spectroscopy, X-ray fiber diffraction, solid-state nuclear magnetic resonance, and molecular dynamics calculations. We show that ccβ-Met forms amyloid-like fibrils of different morphologies on both the macroscopic and atomic levels, which can be controlled by variations of assembly conditions. Interestingly, heterogeneity is also observed along single fibrils. We propose atomic models of the ccβ-Met amyloid-like fibril, which are in good agreement with all experimental data. The models provide a rational explanation why oxidation of methionine residues completely abolishes ccβ-Met amyloid fibril formation, indicating that a small number of site-specific hydrophobic interactions can play a major role in the packing of polypeptide-chain segments within amyloid fibrils. The detailed structural information available for the ccβ model system provides a strong molecular basis for understanding the influence and relative contribution of hydrophobic interactions on native-state stability, kinetics of fibril formation, fibril packing, and polymorphism.