This work presents a single-crystal X-ray diffraction study of an organic co-crystal composed of N-iodo­saccharin and pyridine (NISac·py) under hydro­static pressure ranging from 0.00 (5) GPa to 4.5 (2) GPa. NISac·py crystallizes in the monoclinic system (space group B21/e). The unconventional setting of the space group is adopted (the conventional setting is P21/c, No. 14) to emphasise the strongly pseudo-orthorhombic symmetry of the lattice, with a β angle very close to 90°. The crystal structure contains one molecule each of N-iodo­saccharin (NISac) and pyridine (py) in the asymmetric unit (Z′ = 1), linked via an Nsac...I...N′py halogen-bonding motif. A gradual modification of this motif is observed under pressure as a result of changes in the crystalline environment. Mechanical twinning is observed under compression and the sample splits into two domains, spanning an unequal volume that is mapped by a twofold rotation about the [100] direction of the B21/e unit cell. The twinning is particularly significant at high pressure, being reversible when the pressure is released. The structure of the twinned sample reveals the continuity of a substantial substructure across the composition plane. The presence of this common substructure in the two orientations of the twinned individuals can be interpreted as a structural reason for the formation of the twin and is the first observed example in a molecular crystal. These results indicate that the anisotropy of intermolecular interactions in the crystal structure results in an anisotropic strain generated upon the action of hydro­static compression. Periodic density functional theory calculations were carried out by considering an isotropic external pressure, the results showing good agreement with the experimental findings. The bulk modulus of the crystal was obtained from the equations of state, being 7 (1) GPa for experimental data and 6.8 (5) GPa for theoretical data.