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 (Nb₃ Zr, 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.