Unit-cell lattice parameters have been measured to ~8 GPa in a diamond anvil cell for two single crystals of CaIrO3: one with the perovskite (Pbnm) and the other with the post-perovskite (Cmcm) structure. The CaIrO3 post-perovskite structure is more compressible than the perovskite. A third-order Birch Murnaghan equation of state has been used to fit the measured P-V data with the following refined parameters: V0 = 229.463(8) Å3, K0 = 198(3) GPa, K’ = 1.2(8); and V0 = 226.38(1) Å3, K0 = 181(3) GPa, K’ = 2.3(8) for CaIrO3 perovskite and post-perovskite, respectively. The compressibility of the unit-cell axes of the perovskite structure is highly anisotropic with βa >> βc >> βb. In contrast, the b axis is the most compressible in the post-perovskite structure, whereas the a and c axes have similar compressibilities (with c slightly less compressible than a) and are much stiffer. A comparison between the compressibility of CaIrO3 perovskite and post-perovskite with the isostructural MgSiO3 phases, reveals a similar general behavior, although in detail CaIrO3 perovskite is more and the post-perovskite less anisotropic than the corresponding MgSiO3 compounds.