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Rodríguez started representing Peru during the 2006 FIFA World Cup qualifiers, and quickly became a defensive cornerstone for the national side, representing it at the 2007 Copa América in an eventual quarterfinal exit.
In the 2007 edition held in his country, he helped the national team finish first in the group stage, and scored in the quarterfinals against Uruguay, but in a 1–4 defeat.
However, Baptista was re-called to the Brazil squad for the 2007 Copa América and scored the opening goal in Brazil's 3–0 victory over Argentina in the final on 15 July 2007.
This ended his hopes of playing in the 2007 Copa América and for the national team.
An Uruguayan international since 26 October 2005 in a friendly loss in Mexico, Pereira quickly became a regular for the country, and represented it at the 2007 Copa América.
Aimar scored the last goal of the 2005 FIFA Confederations Cup during Argentina's 1–4 loss in the final to champions Brazil, also appearing with the national side in the 2007 Copa América (losing in the final to the same team, this time 0–3).
After the retirement of fellow countryman Horacio Elizondo he became Argentine's top referee and was selected for the 2007 Copa América where he took charge of three games (Brazil vs Mexico, Brazil vs Ecuador; both group stage and the quarterfinal between Mexico and Paraguay).