Polyelectrolytes with amphiphilic counterions, PEACs, are water insoluble because the amphiphiles self-assemble into highly charged micelles that strongly associate with the equally highly charged polyions. However, in the presence of water soluble cyclodextrins (CDs) that form inclusion complexes with the amphiphiles and prevent micellization, PEACs become soluble as the dispersed amphiphiles behave essentially as simple monovalent counterions. In this paper, we illustrate, by example, how strongly the ternary phase behavior of PEAC:CD:water depends on the polyion flexibility; for a highly flexible polyion (polyacrylate) the amphiphilic aggregates dictate the phase behavior, whereas a much stiffer polyion (DNA) itself dictates liquid crystalline ordering.