A comparative single-crystal X-ray diffraction structure analysis of the family of Al-Cu-Me (Me = Co, Rh and Ir) decagonal quasicrystals is presented. In contrast to decagonal Al-Cu-Co, the other two decagonal phases do not show any structured disorder diffuse scattering indicating a higher degree of order. Furthermore, the atomic sites of Rh and Ir can be clearly identified, while Cu and Co cannot be distinguished because of their too similar atomic scattering factors. The structure models, derived from charge-flipping/low-density elimination results, were refined within the tiling-decoration method but also discussed in the five-dimensional embedding approach. The basic structural building units of the closely related structures are decagonal clusters with 33 Å diameter, which are consistent with the available electron-microscopic images. The refined structure models agree very well with the experimental data.