We have performed structural investigations of ordered kesterite-type Cu2ZnSnS4 up to 30 GPa. Our current X-ray diffraction results clearly excluded the presence of a kesterite - disordered kesterite transition reported previously between 7 and 9 GPa. Nevertheless, specific anomalies connected with the Cu-S bond length of the starting kesterite-type phase are evidenced close to 6 GPa, indicating subtle structural effects at play in this system. Moreover, we have indexed the high-pressure modification of Cu2ZnSnS4 adopted above 16 GPa to a disordered GeSb-type structure, a tetragonally distorted rocksalt-type modification. Full decompression leads to the adoption of a disordered sphalerite/zincblende-type structure. Our complementary density functional theory calculations reproduce accurately the experimental observations and indicate the possibility of a metallic high-pressure GeSb-type phase, unlike the starting semiconducting kesterite-type Cu2ZnSnS4 structure.