At room temperature the bismuth strontium cuprate Bi2.08Sr1.84CuO6 [a = 5.3791 (6), b = 5.3811 (9), c = 24.589 (3) angstrom, beta = 89.93 (1)-degrees, basic space group A2/a, superspace group P(A)2/1/a/1, M(r) = 755.44, D(x) = 7.05 g cm-3, V = 711.7 angstrom3, Z = 4, Cu K-alpha radiation, lambda = 1.541838 angstrom, mu = 1203 cm-1, F(000) = 1278.24, T = 294 K] exhibits a one-dimensional incommensurate modulated structure with a modulation wave-vector q* having components 0.2030 (2), 0, 0.467 (2). Both a displacive modulation wave, acting on all atoms and a density modulation wave, governing the occupancy probabilities of the Bi, Sr and apical O(2) sites are involved in the crystal. 1117 unique hklm reflections with I greater-than-or-equal-to 3-sigma(I) were used to refine the modulated structure. The final R factors (based on F) of main reflections (292), and first- and second-order satellite reflections (563 and 262) are 0.061, 0.061 and 0.086 respectively. The modulation is anharmonic for all atoms. Evolution of the Bi, Sr and apical O(2) site occupancies throughout the crystal is correlated in a spectacular way and shows the existence of Bi and O(2) vacant sites in some unit cells; moreover, some Sr sites are occupied by Bi atoms. These features give rise to various coordinations i.e. square planar, pyramidal, octahedral for copper and from six to nine for strontium. The most likely coordination for bismuth in strontium sites is ninefold coordination; owing to the displacive modulation, both dilute and Bi-condensed regions are found in the crystal. Within the condensed regions, bismuth achieves a classical fourfold coordination. To satisfy the Bi coordination in the Bi-dilute regions it is proposed that extra O atoms have to be introduced either within the Bi-O layers or between two adjacent Bi-O layers.