We demonstrate by finite-difference time-domain simulations in 2D and 3D that optical cavities in realistic finite photonic crystals have lifetimes and modal volumes that are essentially insensitive to disorder (of various types, including surface disorder and randomized positions), even with unphysically large disorder. A lifetime $Q=10^8$ is demonstrates in a 3D single-mode cavity with half-wavelength mode diameter using only eight vertical periods of a disordered crystal.