In 1935 he defeated Hideo Nishimura and Cam Malfroy to reach the third round of the singles event in which he lost to seventh-seeded Roderich Menzel in straight sets.

[3] In 1934 he won the singles title at the Italian Championships in Milan after winning the final against compatriot Giorgio de Stefani in three straight sets.

At Beaulieu and Bordighera, two other tournaments on the Riviera circuit, he was a runner-up in singles, losing the final to Von Cramm and Jean Lesueur respectively.

Palmieri was a member of the Italian Davis Cup team which reached the final of the Europe Zone in 1932 and he compiled a playing record of five wins and five losses.

The tournament was played in a round-robin format and Palmieri finished last, losing all seven of his matches against Henri Cochet, Jan Koželuh, Dan Maskell, Hans Nüsslein, Robert Ramillon, Lester Stoefen and Bill Tilden respectively.