We present compelling evidence pointing to the possible synthesis of unconventional C-66 and C-68 fullerenes in the interior of single-walled carbon nanotubes. The production proceeds from C(60)(-)toluene/benzene clathrates encapsulated inside the nanotubes using heat-driven nanotesttube chemistry. All isomers violate the so-called isolated pentagon rule and are stabilized solely by the proximity of the wall of the host nanotube. We present detailed characterization of the unconventional fullerenes using Raman spectroscopy, C-13 isotope labeling of the benzene molecules, transmission electron microscopy, X-ray diffractometry, and first-principles calculations. Multiple isomers of both C-66 and C-68 are identified in the sample. We argue that our method opens the way to high-yield synthesis of unconventional fullerenes.