Three-dimensional (3D) concentrators for photomultipliers with curved photocathodes have been designed by taking the figures of revolution of ideal two-dimensional (2D) concentrators that are constructed from the 2D profiles of the photocathodes. Two new arguments are presented as to why these 3D concentrators cannot quite reach the maximum concentration factor allowed by the conservation of phase space. Improvements in performance have been obtained by optimizing the collection of off-axis rays and filling the concentrator with a dielectric of suitable refractive index. The complicated optical behavior of the photocathode does not affect concentrator performance.