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DNA condensation in vivo relies on electrostatic complexation with small cations or large histones. We report a synchrotron x-ray study of the phase behavior of DNA complexed with synthetic cationic dendrimers of intermediate size and charge. We encounter unexpected structural transitions between columnar mesophases with in-plane square and hexagonal symmetries, as well as liquidlike disorder. The isoelectric point is a locus of structural instability. A simple model is proposed based on competing long-range electrostatic interactions and short-range entropic adhesion by counterion release.