We present VLBI images of the compact high-luminosity radio galaxy 2352+495 that show symmetric structure on either side of a prominent central core. This contrasts strongly with the asymmetric nuclear structure exhibited by the great majority of powerful extragalactic sources. The outer structure of 2352 + 495 takes the form of two ''mini-lobes'' containing hot spots; in this respect this compact radio galaxy resembles extended radio galaxies, but its overall size, approximately 150 pc, is approximately 1000 times smaller. A reanalysis of existing data on the radio galaxy 0710+439 shows similar compact structure, and together these VLBI images confirm the existence of a class of two-sided compact symmetric objects (CSOs). We show that, in contrast to nuclear radio sources in other powerful objects, the observed structure of CSOs is not dominated by relativistic beaming effects. It is likely that many objects previously classified as ''compact doubles'' will prove to be CSOs when mapped with VLBI with high dynamic range.