Kammala jumla mai zuwa: Córdoba ya jagoranci Colombia don lashe gasar Copa América ta 2001, inda ya zira kwallaye guda daya a wasan karshe. Córdoba kuma ya buga wa kasarsa wasa a gasar cin kofin duniya ta 1998 (ya ɗauki lambar rigar lamba 2 daga Andrés Escobar wanda aka kashe a gasar da ta gabata) ba tare da ya bayyana a wasa ba, FIFA Confederations Cup 2003 (inda suka gama a matsayi na hudu), da kuma wasu bugu uku na Copa América (
1997, 1999, da kuma 2007).