They made a particularly healthy contribution in 1993, by reaching the final, and in 2007, when they beat Brazil and thumped Paraguay 6-0 before eventually losing to a Lionel Messi-inspired Argentina in the semi-finals.
This time, however, the tournament takes place immediately before their own confederation's Gold Cup tournament in the United States, which naturally gets priority.
As a result, coach Miguel Herrera has been forced to bring what is effectively a B team, choosing from players who are on the fringe of the senior squad.
These include 36-year-old central defender Rafael Marquez, who has played at four World Cups, and Atletico Madrid striker Raul Jimenez.
The Copa America has been blighted in the past by poor organisational decisions and the presence of a reserve team among the finalists can only devalue the tournament.
It also raises the question of why the Mexican federation accepted the invitation in the first place.
(Writing by Brian Homewood; Editing by Ken Ferris)
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