From the wide-angle, equatorial X-ray data of a beta-amyloid analogue, we previously calculated the electron density of the constituent beta-crystallite, which assembles as multimers (four to six crystallites) in building the amyloid fibre. In the scattering region where the spacing d < approximately 10 A, the observed reflections were indexed by an orthogonal lattice with a unit cell having a = 9.44 A, b = 6.92 A and c = 10.76 A. The phases were initially derived from the atomic coordinates of the beta-keratin backbone and were optimized by including new peaks (as point atom or sphere) in the subsequent Fourier iteration. The R-factor between the observed and calculated amplitudes was refined to 35%. In further developing our analysis, we have now applied an alternative constraint to the optimization by eliminating the negative electron densities, and found that the R-factor decreased to 19% after three iterations. The refined electron density map fits phenylalanine, indicating that the amyloid core likely comes from the hydrophobic Leu-Val-Phe-Phe residues. We have applied the same type of optimization, using beta-silk as an initial phase model, to the hydrophobic H1 domain of the prion protein for which the monoclinic unit cell constants are a = 9.51 A, b = 7.06 A, c = 15.94 A and beta = 88.4 degrees. The R-factor decreased to 11% from 64% after two iterations. The electron density map shows a silk-like quarter-staggered arrangement of beta-sheets which, in the intersheet direction, have circular peaks in one beta-sheet and elongated peaks in the alternating beta-sheet. These peaks were interpreted as arising from the C-terminal alanine-rich domain and N-terminal hydrophobic residues. Skeletal atomic models for these core regions support this interpretation.