Single-crystal X-ray investigations of potassic high cordierite revealed reflections not compatible with space group P6/mcc, which is the space group previously accepted for all high cordierite. To obtain single crystals large enough for a structure determination using X-ray intensities, K-bearing high cordierite samples were synthesized from glass. After measuring X-ray intensities on a single-crystal diffractometer, the structure was refined in a number of subgroups of P6/mcc. The comparisons between the resulting R values and structure descriptions lead to the conclusion that only space group P6 can describe the framework deformations induced by the presence of K in the structural channels at z ≈ 0.14, which is a position of low symmetry. The redetermination of the space group of other high cordierite crystals either free of alkalis or containing Na or Cs revealed no deviation from space group P6/mcc. The refined structure of Cs-bearing high cordierite displayed framework deformations as a consequence of the presence of Cs in structural channels at (0,0¼). The high symmetry of this position does not lead to asymmetric forces on the framework, thus preserving the space group P6/mcc.