By decoupling the mechanical behaviour of building units for the first time in a wine-rack framework containing two different strut types, we show that lithium L-tartrate exhibits NLC with a maximum value, K_max = −21 TPa⁻¹, and an overall NLC capacity, χ_NLC = 5.1%, that are comparable to the most exceptional materials to date. Furthermore, the contributions from molecular strut compression and angle opening interplay to give rise to so-called “hidden” negative linear compressibility, in which NLC is absent at ambient pressure, switched on at 2 GPa and sustained up to the limit of our experiment, 5.5 GPa. Analysis of the changes in crystal structure using variable-pressure synchrotron X-ray diffraction reveals new chemical and geometrical design rules to assist the discovery of other materials with exciting hidden anomalous mechanical properties.