The concentration and distribution of heavy minerals in tsunami deposits is not random and mostly source-dependent. Heavy minerals may thus be good indicators of sediment provenance and tsunami flow dynamics. The tsunamis generated by the 1996 phreato-magmatic eruption in Karymskoye Lake represent a relevant case-study because the provenance of the abundant heavy minerals found in the tsunami deposits is well constrained (the on-going basaltic eruption itself). X-ray computed tomography (X-CT) of cores of tsunami sediments is used to identify heavy minerals and characterise their source and spatial distribution in the tsunami deposit, and to propose a scenario of the coupled eruption and tsunamis. An original combination of methods including X-CT, SEM and XRF core scanner allows distinguishing subunits corresponding to pulses of sediments deposition and associated inputs of heavy minerals, together with erosive contacts, laminations, and rip-up clasts of the substratum. The structure of the tsunami deposits suggests that a major tsunami consisting of two main waves inundated the coastal terrace up to 100m inland on the eastern shore of the lake; a scenario that is consistent with waves generated by experimental explosions. This largest tsunami might have occurred when underwater explosions were at a critical water depth of 40m (corresponding to a two-third submerged explosion in the 60m deep lake). However, more investigations are needed to better understand the critical conditions leading to a tsunami during underwater eruptions.