The contemporary security environment in Europe is radically different from the one during the Cold War. New challenges ranging from political propaganda, meddling into democratic elections, terrorism, cyber warfare, weaponisation of energy resources, or asymmetric warfare of little green men preoccupies many countries in Europe. How to deter activities associated with these challenges and threats remains a puzzle. This paper tries to resolve this puzzle by overcoming the Cold War binary thinking on deterrence as involving either punishment or denial. In order to achieve that, it updates the logic of deterrence by introducing interactions in time, which are then related to the concept known as a cumulative deterrence. Such an analytical framework enables Europe to face hybrid threats in a more pragmatic and realistic way.