The Cumbre Vieja volcano, on La Palma in the western Canary Islands, is an unstable area that may develop into a future landslide, generating a tsunami that could cause damage far from the source. However, volcaniclastic turbidites that are directly correlated with the two most recent Canary Islands landslides, show stacked sub-units within a single turbidite bed. This may indicate multiple stages of landslide failure. Similar findings have previously been reported from volcaniclastic turbidites linked to Hawaiian landslides. Consequently the potential tsunami hazard from such failures may be lower than previously predicted.