PACS 42.70.Qs -Photonic bandgap materials PACS 42.55.Sa -Microcavity and microdisk lasers PACS 42.50.Pq -Cavity quantum electrodynamics Abstract -Defect cavities in 3D photonic crystal can trap and store light in the smallest volumes allowable in dielectric materials, enhancing non-linearities and cavity QED effects. Here, we study inverse rod-connected diamond (RCD) crystals containing point defect cavities using planewave expansion and finite-difference time domain methods. By optimizing the dimensions of the crystal, wide photonic band gaps are obtained. Mid-bandgap resonances can then be engineered by introducing point defects in the crystal. We investigate a variety of single spherical defects at different locations in the unit cell focusing on high-refractive-index contrast (3.3:1) inverse RCD structures; quality factors (Q-factors) and mode volumes of the resonant cavity modes are calculated. By choosing a symmetric arrangement, consisting of a single sphere defect located at the center of a tetrahedral arrangement, mode volumes < 0.06 cubic wavelengths are obtained, a record for high index cavities.