It is a particular challenge to develop a stigmatic spectrograph for EUV wavelengths since the very low normal-incidence reflectance of standard materials most often requires that the design be restricted to a single optical element which must simultaneously provide both re-imaging and spectral dispersion. This problem has been solved in the past by the use of toroidal gratings with uniform line-space rulings (TULS). A number of solar EUV spectrographs have been based on such designs, including SOHO/CDS, Solar-B/EIS, and the sounding rockets SERTS and EUNIS. More recently, Kita, Harada, and collaborators have developed the theory of spherical gratings with varied line-space rulings (SVLS) operated at unity magnification, which have been flown on several astronomical satellite missions. These ideas are now combined into a spectrograph concept that considers varied-line space grooves ruled onto toroidal gratings. Such TVLS designs are found to provide excellent imaging even at very large spectrograph magnifications and beam-speeds, permitting extremely high-quality performance in remarkably compact instrument packages. Optical characteristics of two solar spectrographs based on this concept are described: SUMI, proposed as a sounding rocket experiment, and NEXUS, proposed for the Solar Dynamics Observatory mission.