The first combined high pressure single-crystal X-ray diffraction and high pressure magnetism study of two polymetallic clusters is presented in an attempt to correlate the observed changes in structure with changes in magnetic response without the need for changes in external ligation. At 1.5 GPa the structure of [Mn(6)O(2)(Et-sao)(6)(O(2)CPh(Me)(2))(2)(EtOH)(6)] (1; Et-saoH(2) = 2-hydroxyphenylpropanone)--a single molecule magnet (SMM) with an effective anisotropy barrier of approximately 86 K--and of [Mn(6)O(2)(Et-sao)(6)(O(2)C-naphth)(2)(EtOH)(4)(H(2)O)(2)] 2 both undergo significant structural distortions of their metallic skeletons, which has a direct effect upon the observed magnetic response. The application of hydrostatic pressure on the two compounds (up to 1.5 GPa) flattens the Mn-N-O-Mn torsion angles weakening the magnetic exchange between the metal centres. In both compounds one interaction switches from ferro- to antiferromagnetic, with the Jahn-Teller (JT) axes compressing (on average) and re-aligning differently with respect to the plane of the three metal centres. High pressure dc chi(M)T plots display a gradual decrease in the low temperature peak height and slope, simulations showing a decrease in |J| with increasing pressure with a second antiferromagnetic J value required to simulate the data. The "ground states" change from S = 12 to S = 11 for 1 and to S = 10 for 2. Magnetisation data for both 1 and 2 suggest a small decrease in |D|, while out-of-phase (chi(M)(//)) ac data show a large decrease in the effective energy barrier for magnetisation reversal.