In October 1985, Alfa was dispatched to Beirut, Lebanon, when four Soviet diplomats had been taken hostage by a Sunni militant group. By the time Alfa was onsite, one of the hostages had already been killed. The perpetrators and their relatives were identified by supporting KGB operatives, and the relatives were taken hostage. Following the standard policy of 'no negotiation', Alfa proceeded to sever some of their hostages' body parts and sent them to the perpetrators with a warning that more would follow if the Russian hostages were not released immediately. The tactic was a success and no other Russian national was taken hostage in the Middle East for the next 20 years, until the 2006 abduction of Russian diplomats in Iraq.

Regarding the 2006 kidnapping:

After clandestine negotiations failed to secure the men's release, Soviet agents grabbed half a dozen fundamentalists in West Beirut and reportedly sliced off a few of their fingers, sending the severed digits to the fundamentalist leadership with the message: "Release our people or you'll get your people back piece by piece."