The structural evolution of Tl-exchanged natrolite with idealized formula Tl2[Al2Si3O10]·2H2O, compressed in penetrating (water:ethanol 1:1) and non-penetrating (paraffin) media, was studied up to 4 GPa. The presence of Tl+ with non-bonded electron lone pairs, which can be either stereo-chemically active or passive, determines distinctive features of the high-pressure behavior of the Tl-form. The effective volume of assemblages Tl+(O,H2O)n depends on the E-pairs activity: single-sided coordination correlates with smaller volumes. At ambient conditions, there are two types of Tl positions, only one of them having a nearly single-sided coordination as a characteristic of stereo-activity of the Tl+ E pair. Upon the compression in paraffin, a phase transition occurs: a 5% volume contraction of flexible natrolite framework is accompanied by the conversion of all the Tl+ cations into stereo-chemically active state with a single-sided coordination. This effect requires the reconstruction of all the extra-framework subsystems with the inversion of the cation and H2O positions. The compression in water-containing medium leads to the increase of H2O content up to three molecules pfu through the filling of partly vacant positions. This hinders a single-sided coordination of Tl ions and preserves the configuration of their ion-molecular subsystem. It is likely that the extra-framework subsystem is responsible for the super-structure modulation.