Seven criteria are developed and discussed that lead to the design of a new enediyne anticancer drug, which should have low toxicity but high biological selectivity and activity when attacking the DNA of tumor cells. These criteria concern (among others) the thermodynamic and kinetic stability of the species involved in the reaction of an enediyne, the biradical character and H-abstraction ability of the intermediate biradical generated in a Bergman reaction of the enediyne, and the basicity of the enediyne and its associated biradical. Thirteen different heteroenediynes were investigated with the help of B3LYP/6-31G(d,p) calculations to find a suitable candidate for a new enediyne anticancer drug, which fulfills the seven criteria. These calculations included the determination of reaction profiles for Bergman and retro-Bergman reactions, the calculation of singlet-tripler splittings of biradicals formed from enediynes, and the prediction of pK(a) values. Results were tested by using a larger basis set (6-311+G(3df,3pd)), another functional (BLYP), and coupled cluster methods such as CCSD(T) and the Brueckner orbitals-based BD(T) method. The best candidate for a new enediyne anticancer drug is an N,C-dialkynyl aldimine incorporated into a cyclodecaene ring.