Summary: Using extensive Molecular Dynamics simulations we study the behavior of very rigid polyelectrolytes with hydrophobic side chains that are known to form cylindrical micelles in aqueous solution. We investigate the stability of such micelles with respect to hydrophobicity, Coulomb interaction, and micellar size. We show that for the parameter range relevant for poly(p‐phenylene sulfonate)s (PPP) one finds a stable finite micellar size close to the experimental parameter region. We also point out that our model has some similarities to DNA solutions with added condensing agents, hinting to the possibility that the size of DNA aggregates is under certain circumstances thermodynamically limited.