This work investigates the Jahn-Teller (JT) distortion in different Mn3+ fluoride series by optical absorption (OA) spectroscopy. The aim is to establish correlations between the local structure of the formed MnF63- derived from x-ray diffraction and the JT splitting associated with the parent octahedral E-5(g)(3z(2)-r(2),x(2)-y(2)) and T-5(2g)(xy,xz,yz) states, Delta(e) and Delta(t), obtained from the OA spectrum. A salient feature is the linear relation exhibited by both Delta(e) and Delta(t) with the tetragonal coordinate Q(theta) along the whole series. From these relations we derive suitable electron-ion coupling coefficients related to the E-5(g) and T-5(2g) states whose values play a key role in the exE and exT JT theory, respectively. The results of these correlations are applied to investigate the structural variations undergone by the two-dimensional compounds NaMnF4 and TlMnF4 under pressure using OA spectroscopy. Interestingly, the analysis carried out is relevant since it provides useful information on the Mn3+ local structure, a task that is difficult to achieve using extended x-ray-absorption fine structure under pressure due to the high absorption of the diamond anvils. We conclude that the effect of pressure in NaMnF4 is to reduce progressively the JT distortion of the complex, keeping its tetragonal symmetry. The pressure effects in TlMnF4 are more drastic, leading to pressure-induced structural phase transitions of low symmetry. At variance with NaMnF4, the high-pressure Mn3+ local structure seems to have significant rhombic distortions. (C) 2003 American Institute of Physics.