Pure silica ITW zeolite can be synthesized using 1,2,3-trimethylimidazolium and 1,3-dimethylimidazolium cations and fluoride anions as structure-directing agents (SDAs). Similarly to the previously reported 1,3,4-trimethylimidazolium, the dimethyl cation can also produce the zeolite TON, but this higher framework density phase finally transforms in situ into ITW. The structures of the as-made and calcined phases prepared with the new cations show a unit cell doubling along z, and the refined structures are reported. Periodic Density Functional Theory calculations provide the energies of the six SDA-ITW and SDA-TON zeolites, and their relative stabilities fully agree with the experimental observations. Structure-direction in this system is discussed from experimental and theoretical results that give strong support to the idea that strained silica frameworks are made possible in fluoride media by decreasing the covalent character of the Si-O bond. This decreased covalency is enhanced with the 1,2,3-trimethyl isomer, which is shown to be the strongest SDA for ITW and, at the same time, is the more hydrophilic of the three SDAs tested. Our observations with the three SDAs agree with the so-called Villaescusa's rule, i.e., the low framework density phase is favored at higher concentrations, but at the same time question the supersaturation hypothesis that has been proposed to explain this rule, since here the low-density phase is the most stable one.