The aggregation of the intrinsically disordered protein alpha-synuclein (αS) into amyloid fibrils is thought to play a central role in the pathology of Parkinson's disease. Using a combination of techniques (AFM, UV-CD, XRD, and amide-I 1D- and 2D-IR spectroscopy) we show that the structure of αS fibrils varies as a function of ionic strength: fibrils aggregated in low ionic-strength buffers ([NaCl] ≤ 25 mM) have a significantly different structure than fibrils grown in higher ionic-strength buffers. The observations for fibrils aggregated in low-salt buffers are consistent with an extended conformation of αS molecules, forming hydrogen-bonded intermolecular β-sheets that are loosely packed in a parallel fashion. For fibrils aggregated in high-salt buffers (including those prepared in buffers with a physiological salt concentration) the measurements are consistent with αS molecules in a more tightly-packed, antiparallel intramolecular conformation, and suggest a structure characterized by two twisting stacks of approximately five hydrogen-bonded intermolecular β-sheets each. We find evidence that the high-frequency peak in the amide-I spectrum of αS fibrils involves a normal mode that differs fundamentally from the canonical high-frequency antiparallel β-sheet mode. The high sensitivity of the fibril structure to the ionic strength might form the basis of differences in αS-related pathologies.