The structures of the third and fifth generation of a liquid crystal dendrimer have been studied as a function of temperature and pressure using X-ray diffraction. The third generation LC dendrimer showed a crystal to smectic transition and increasing pressure simply increased the transition temperature. The fifth generation showed two different rectangular columnar phases and one hexagonal columnar phase. The application of pressure did not induce either of the rectangular phases to transform to a simple smectic phase, suggesting that they are slightly modified smectic phases. The hexagonal phase was more easily suppressed by the application of pressure, suggesting that the molecules are splayed into a disc-like conformation and become more cylinder-like under pressure.