During the last few decades, joint investigations of microgravity and surface deformation measurements have played an increasingly important role in studying the internal dynamics of active volcanoes. Deformation and microgravity observations have been accomplished at Mt Etna since the eighties. Past data sets collected during important paroxysmal events can be utilized as case-studies to both (1) test the possibilities of nowadays more powerful inversion tools and improved analytical formulations to model the source-mechanisms of volcano-related deformation and gravity changes and (2) in turn obtain new insights into the functioning of the plumbing system of the volcano. Here we analyze a data set spanning the March 1981 eruption of Mt. Etna. Large horizontal displacements were evidenced on the NE and SW flanks of the volcano through electrooptical distance measurements (EDM) during two 20-month periods, both encompassing the March 1981 eruption. Elevation changes, evidenced through leveling measurements, during a 12-month period spanning the eruption, were in general smaller than horizontal displacements with important amplitudes only close to the eruptive fissure. Gravity measurements, carried out together with leveling measurements, evidenced positive changes, spatially well correlated with elevation changes, but having a larger wavelength. The joint inversion of the multimethod geophysical data is regarded as a multiobjective optimization problem and solved through a Genetic Algorithm technique of the nondominated type. We conclude that a composite intrusive mechanism with two tensile cracks, each associated to a zone where preexisting microfractures were filled with new magma, leaded to the 1981 eruption. The results of the present study highlight the advantages of multiobjective evolutionary algorithms, as a powerful tool to jointly invert multimethod geophysical data, and pose important issues on the subject of volcano-monitoring.