We report on measurements of the evolution of the magnetization [M] upon warming from T-0 (4.2 or 77 K) to T-c for type II superconductors with the locus of [M] initially situated along bridges between the envelopes of the major hysteresis curves. Strongly hysteretic and semi-reversible specimens of low and high T-c type II superconductors have been studied (Nb3Zr, VTi, YBCO, Nb and BiSCCO). Concentric, oppositely directed magnetic moments coexist in the specimens when [M] lies along the bridges. We focused on the cases where [M] = 0, hence, before warming, the constituent moments cancel each other exactly. Since they diminish in magnitude at different rates as T is increased to T-c, their sequential 'release' leads to a rich variety of phenomena. A simple model exploiting the critical state, an equilibrium Meissner current and conservation of flux accounts for all the intricate behaviour encountered.