A detailed study, by x-ray diffuse scattering, of the recently found two-dimensional ͑2D͒ displacive shortrange-order ͑2DSRO͒ superstructure, with doubled periodicity along the orthorhombic a o direction and perpendicular to the known long-range structural modulation, from the high-T c superconductor Bi 2 Sr 2 CaCu 2 O 8+␦ ͑Bi-2212͒ is reported. The investigation has been extended to high and low temperatures for optimally doped crystals, to crystals with different doping levels, and to the one layer compound Bi 2 Sr 2 CaCu 2 O 6+␦ ͑Bi-2201͒. The results show that the 2DSRO is present at room temperature, for all studied crystals and with the same commensurate 2a o periodicity; significant differences in intensity and in the extent of the 2DSRO are however observed. The most striking feature is that both, the intensity of the diffuse scattering and the extent of the 2DSRO goes through a maximum for the optimal doped crystals and decreases for overdoped and underdoped samples, they are also smaller for the one layer Bi-2201 which has a lower T c . The reversible temperature dependence reveals that the diffuse scattering is unchanged between 35 K and 300 K, but starts washing out for higher temperatures and vanishes around 450 K, temperature above which another scattering, one dimensional in character, is found. This one-dimensional ͑1D͒ short-range order ͑1DSRO͒ corresponds to linear correlated displacements along the pseudotetragonal directions of the Cu-O-Cu chains. These findings tend to show that these short-range ordering features may be of importance for a better understanding of high-T c materials, at least those from the bismuth-based family.