Since the DAMA/LIBRA collaboration released updated results from their search for the annual modulation signal expected from Dark Matter (DM) scattering in their NaI detectors, we have fitted the updated DAMA result for the modulation amplitudes for a Weakly Interacting Massive Particle (WIMP) signal, parameterizing the interaction with nuclei in terms of the most general effective Lagrangian for a WIMP particle spin 1/2, systematically assuming dominance of one of the 14 possible interaction terms and a standard Maxwellian for the WIMP velocity distribution. We find that most of the couplings of the non-relativistic effective Hamiltonian can provide a better fit compared to the standard Spin Independent interaction case, and with a reduced fine-tuning of the three parameters (WIMP mass, WIMP-nucleon effective cross-section and ratio between the WIMP-neutron and the WIMP-proton couplings). In addition, effective models for which the cross section depends explicitly on the WIMP incoming velocity can provide a better fit of the DAMA data at large values of $m_{\chi}$ compared to the standard velocity-independent cross-section due to a different phase of the modulation amplitudes. All the best fit solutions are in tension with exclusion plots of both XENON1T and PICO60.