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We present a source solution for the tsunami generated by the Mw 6.6 earthquake that occurred on 2 May 2020, about 80 km offshore south of Crete, in the Cretan Passage, on the shallow portion of the Hellenic Arc subduction zone (HASZ). The tide gauges recorded this local tsunami on the southern coast of Crete and Kasos island. We used Crete tsunami observations to constrain the geometry and orientation of the causative fault, the rupture mechanism, and the slip amount. We first modelled an ensemble of synthetic tsunami waveforms at the tide gauge locations, produced for a range of earthquake parameter values as constrained by some of the available moment tensor solutions. We allow for both a splay and a back-thrust fault, corresponding to the two nodal planes of the moment tensor solution. We then measured the misfit between the synthetic and the Ierapetra observed marigram for each source parameter set. Our results identify the shallow, steeply dipping back-thrust fault as the one producing the lowest misfit to the tsunami data. However, a rupture on a lower angle fault, possibly a splay fault, with a sinistral component due to the oblique convergence on this segment of the HASZ, cannot be completely ruled out. This earthquake reminds us that the uncertainty regarding potential earthquake mechanisms at a specific location remains quite significant. In this case, for example, it is not possible to anticipate if the next event will be one occurring on the subduction interface, on a splay fault, or on a back-thrust, which seems the most likely for the event under investigation. This circumstance bears important consequences because back-thrust and splay faults might enhance the tsunamigenic potential with respect to the subduction interface due to their steeper dip. Then, these results are relevant for tsunami forecasting in the framework of both the long-term hazard assessment and the early warning systems. [ABSTRACT FROM AUTHOR]