The Myers-Saito and the C-2-C-6 cyclization ("Schmittel" cyclization) of the parent enyne-allene (Z)-1,2,4-heptatriene-6-yne were investigated with pure density functional theory (DFT) methods and were compared to coupled cluster [CCSD(T)] and Brueckner doubles [BCCD(T)] high-level calculations. Both the Becke-Lee-Yang-Parr (BLYP) and the Becke-Perdew-Wang (BPW91) DFT levels with the 6-31G(d) basis sets are quite suitable to describe the cyclization barriers and are nearly as accurate as much more time-consuming high-level methods. As noted before for the Bergman-cyclization, the hybrid functional B3LYP yields good geometries but is less suitable for energies due to Hartree-Fock mixing. Single-point energy evaluations with the much larger cc-pVTZ basis set do not necessarily improve the results; some even become worse. The computed enthalpy of formation (Delta H(f)degrees) of the Myers-Saito product (107 +/- 4 kcal mol(-1)) compares relatively well to the experimental value (103 +/- 3 kcal mol(-1)) where an upward correction within the error bars seems indicated. Using isodesmic equations, the Delta H(f)degrees of the Schmittel product is predicted to be 129 +/- 3 kcal mol(-1). Since BLYP describes the barriers of the parent enyne-allene system quite well, it was utilized to compute the cyclizations of monocyclic enyne-allenes (ring sizes = 7-10 carbons). The Myers-Saito cyclization of the nine-membered ring is associated with the smallest reaction barrier and the highest exothermicity. While ring strain effects are not able to favor the Schmittel products much over the Myers-Saito products, the eight-membered ring closures should give rise to a mixture of both products. The singlet-triplet separations of all cyclization products are very small (1 kcal mol(-1)); the hydrogen-abstracting ability of such cyclic systems should therefore be rather high.