We examine the superconductivity-induced redistribution of optical spectral weight in Bi2Sr2CaCu2O8 near optimal doping using a detailed Kramers-Kronig consistency analysis of the kink (slope change) at T-c of the temperature-dependent optical spectra, published earlier [H. J. A. Molegraaf , Science 295, 2239 (2002)]. We demonstrate that the temperature dependence of the complex dielectric function at high frequencies (above 0.75 eV) imposes the most stringent limits on the possible changes of the low-frequency integrated spectral weight. The presented calculations provide additional arguments, supporting the previous conclusion about a superconductivity-induced increase of the integrated low-frequency spectral weight below T-c. The Ferrell-Glover-Tinkham sum rule is not satisfied well above 2.5 eV, which indicates that this increase is caused by the transfer of spectral weight from the interband to the intraband region and only partially by the narrowing of the Drude peak.