This paper deals with the central stars of two large, low-surface-brightness planetary nebulae: V605 Aquilae, central star of Abell 58, and 0950+139, central star of EGB 6. Both of these nuclei are associated with compact emission-line nebulosities, which are unresolved from the ground. We obtained images with the Faint Object Camera (FOC) on the Hubble Space Telescope of both objects, in order to determine the nature of the compact nebulae.