Rodríguez then tried his luck with boleros and recorded various albums, which gave way to various hit songs, particularly "Inolvidable" (Unforgettable), composed by Julio Gutiérrez, and "En La Soledad", (In Solitude), composed by Puchi Balseiro, which are considered by many to be his most successful songs.
Josip Broz Tito | Tito Puente | Robert Rodriguez | Alex Rodriguez | Iván Rodríguez | Tito Ortiz | José Luis Rodríguez Zapatero | Tito Gobbi | Paul Rodriguez | Tito Santana | Omar Rodríguez-López | Tito Schipa | Tito Nieves | Silvio Rodríguez | La clemenza di Tito | Dennis Tito | Tito Sotto | Tito Fuentes | Pedro Rodríguez | Miguel Ángel Rodríguez | John Rodriguez | Felix Rodriguez | Carrie Rodriguez | Tito Rojas | Tito Capobianco | Spain Rodriguez | Narciso Rodriguez | Félix Rodríguez (Central Intelligence Agency) | Tito Rodríguez | Tito Alonso |
Among the musicians who played in Curbelo's band were Candido, Tito Puente, and Tito Rodriguez; the group split time between New York and Miami, and played in some of both cities' top nightclubs and ballrooms.
He moved to United Artists Records in the early 1960s, where he contributed to many compilations of movie themes, released albums under his own name and backed a succession of singers, notably Connie Francis, Gloria Lynne, Shirley Bassey and Puerto Rican singers like Tito Rodríguez and Chucho Avellanet.
Acts by Tito Rodríguez and his band and from trios such as Trio Los Duques, Trio Borincano, Los Panchos, and Vegabajeño were often seen.