Very recently, narrow nanotubes have been observed with a diameter of 5 Å and even with a diameter of 4 Å. It has been supposed that the narrow nanotubes are closed by fragments of C36 and C20 fullerenes. The contribution reports computations on related model nanotubes with stoichiometries like C84, C96 or C80. Computations are carried out at the PM3 (Parametric Method 3), SaM1 (Semi-Ab-Initio Model 1), HF/4-31G (Hartree-Fock SCF approach with the standard 4-31G basis set), and B3LYP/6-31G* (Becke's three parameter functional with the non-local Lee-Yang-Parr correlation functional using the standard 6-31G* basis set) levels, though the geometry optimizations are performed only at the semiempirical levels. Two C36 fullerenes are considered, D6h and D2d, and, for example, at the PM3 level and with the C84 nanotube stoichiometry the D2d cage closure gives a lower energy (by 185 kcal/mol and diameter of 5.42 Å). There is another possible candidate, C32 cage with a D4d symmetry. At the PM3 level and with the C96 nanotube stoichiometry the D4d closure has the nanotube enrgy lower by 210 kca/mol (with the nanotube diameter of 5.43 Å) compared to the D6h nanotube closure. On the other hand, four-membered rings should not play a significant role in the narrow nanotubes with the diameter of 4 Å, where the dodecahedron-related closure should be exclusive as a four-membered ring containing structure is located already much higher in energy.