In studying the statistical frequency of exchange in comparison-exchange (CE) networks we discover a new elementary form of comparison-exchange which we name the "2-op". The operation supports concurrent and non-interfering operations of two traditional CEs upon one shared element. More than merely improving overall statistical performance, the introduction of NICE (non-interfering CE) networks lowers long-held bounds in the number of stages required for sorting tasks. Code-based CEs also benefit from improved average/worst case run time costs.