"Addormentarmi così" is a 1948 song written by the Italian lyricist Ornella Ferrari, to music by Vittorio Mascheroni [it] for the singer Lidia Martorana [it] with an arrangement of Pippo Barzizza.
[1] The lyrics begin: «Addormentarmi così/ fra le tue braccia/ mentre tu mi baci /mi baci sempre più...».
[2] The song is considered an Italian classic and was covered by dozens of artists, including Adriano Celentano, Teddy Reno, Gigliola Cinquetti, Luciano Tajoli, Betty Curtis, Flo Sandon's, Lara Saint Paul.
[1] It was introduced to an American audience by Frankie Laine in 1958 in his first album with Michel Legrand, A Foreign Affair.