We report on a distortion of Bi2Sr2CanCun+1 O6+2n+x (n = 0,1) single crystals, perpendicular to the CuO2 planes (the c-axis), for non-stoichiometric samples containing an excess of Bi. The distortion involves two parts: (a) symmetric displacements in the SrO and CuO2 planes along the c-axis, and (b) an antisymmetric longitudinal compressive wave. The latter is revealed by observing odd harmonics in the X-ray diffraction (XRD) data. Such odd harmonics are typically extinguished for the 14/mmm space group of the exact stoichiometric phase. The antisymmetric compressive wave is reported for both BSCCO-2201 and BSCCO-2212 Bi excess samples, as well as for La-doped BSCCO-2201 samples. We have performed XRD model calculations for all samples studied, combined with Fourier analysis of the periodic c-axis modulation. The antisymmetric compressive wave was proven by reconstructing the atomic position profile from the intensity of odd XRD peaks caused by this commensurate modulation. Our results indicate preferential ordered substitution of Bi ions on nominally Sr ion positions. We also discuss implications for oxygen mobility, reversible sample doping, and electronic properties. (C) 2001 Elsevier Science B.V. All rights reserved.