 During her deployment to the Mediterranean Sea in the summer of 1958, "Basilone" joined other 6th Fleet units in patrolling the coast of Lebanon in response to internal political upheavals in that country.In 1962, however, a break came in her east coast-Mediterranean cycle of operations.After conducting local ASW exercises during mid-January and making a futile round-trip voyage to Mayport, Florida, and back late in the month to support the recovery of Col. John Glenn's Mercury flight which had to be delayed because of weather and technical difficulties, "Basilone" again departed Norfolk on 17 February along with her eight DesRon 36 squadron mates to rendezvous with the aircraft carrier for the voyage across the Atlantic.