Magnetization measurements on many single crystals of YBaCuO as well as BiSrCaCuO show a non-vanishing remanent magnetization in a region where the field-cooled and zero-field-cooled magnetizations coincide. We call this kind of remanence "residual irreversibility". We argue that this behavior is not compatible with over-simplified critical-state models or surface barriers. We show how it can arise from weak "residual" pinning in a regime where vortices are further apart than the penetration depth and the reversible B(H) curve shows a sharp initial rise just above Hcl. The "residual irreversibility" can be enhanced in crystals with an inhomogeneous or non-superconducting core, as seen in some of our thicker YBa/CuO crystals and also in BiSrCaCuO. We also show how the field-cooled Meissner fraction can measure the superconducting volume fraction in the low-field limit. © 1990.