This paper is a Second-Law study of thermal insulation systems consisting of two 1-dim. insulations in parallel. It is shown that the parallel-insulation model applies to power and refrigeration systems exposed to large absolute temperature ratios. The insulation design which conserves maximum exergy (available work) is determined for two classes of parallel-insulation systems: in one class, the two parallel insulations are cooled continuously by two streams, in the other class they are cooled partly (intermittently) by one stream of single-phase fluid. The study shows that, in contradiction to previously published results, the continuous-cooling method is thermodynamically superior to the partial-cooling method. © 1983.