The magnetization around the superconducting transition was measured in a Tl 0.5 Pb 0.5 Sr 2 CaCu 2 O 7 crystal affected by a considerable reduction ͑ϳ55% ͒ of its effective superconducting volume fraction but still with a relatively sharp low-field Meissner transition, a behavior that may be attributed to the presence of structural inhomogeneities. By taking into account these inhomogeneities just through the Meissner fraction, the observed diamagnetism may still be explained, consistently above and below the superconducting transition, in terms of the conventional Ginzburg-Landau approach with fluctuations of Cooper pairs and vortices.The behavior of the magnetization around the Meissner transition provides an unavoidable constraint for any phenomenological description of a superconducting transition. 1 In the last few years, various groups have reported the observation of strong anomalies in the magnetization measured around the superconducting transition in high-T C cuprate superconductors ͑HTSCs͒ with different doping levels. Among these anomalies are the observation under low fields of giant diamagnetism ͓with amplitudes of orders of magnitude larger than the one associated with superconducting fluctuations in the conventional Ginzburg-Landau ͑GL͒ scenario͔ and a seemingly nonlinear temperature behavior of the associated upper critical field H C2 ͑T͒ near T C . 2-4 The origin of this unconventional ͑non-GL͒ behavior is at present a debated issue, 2-14 the proposals including T C inhomogeneities or vortex fluctuations even well above the measured T C . The interest of this debate is enhanced by the fact that it also concerns other open aspects of the HTSCs,such as the pseudogap in the normal state or the possible existence of a vortex fluid over a wide temperature range above T C . 14-16The magnetization measurements and analyses performed recently by our group in different HTSCs and dirty low T C superconductors ͑without nonlocal electrodynamic effects͒ favor the presence of extrinsic T C inhomogeneities, just associated with chemical inhomogeneities, as the origin of most of the observed magnetization anomalies. 4,12,17,18 Nevertheless, there is another very common type of inhomogeneity whose influence on the magnetization also deserves a close inspection: the one associated with structural defects at different length scales, including those as smaller as a few times the superconducting coherence length amplitude ͑0͒. In extreme type II superconductors, even these short length inhomogeneities, difficult to be directly observed, may strongly decrease the effective superconducting volume fraction without enlarging the temperature width of the low-field Meissner transition. In this Brief Report, we will first present detailed magnetization measurements around the Meissner transition in a Tl 0.5 Pb 0.5 Sr 2 CaCu 2 O 7 ͑TlPb1212͒ crystal deeply affected by a reduction of the effective volume fraction, an effect which does not enlarge the temperature width of the low-field Meissner transition and that may be a...