Micellar-like solutions consisting of macroions with 60 negative elementary charges with short flexible counterions were studied by Monte Carlo simulations. The structure of the systems was considered as a function of the properties of the flexible counterions and the macroion density. At increasing charge of the flexible counterions, a reduced macroion-macroion repulsion is observed and eventually the system phase separates. The effects are similar to that found for simple multivalent counterions, but weaker, originating from spatial correlations between counterions residing on different macroions. Another type of reduced phase stability appears as the separation between the charges in a flexible dimer increases; now the reduced stability is induced by counterions bridging pairs of macrions.