Valdez akamiririra Paraguay mumakwikwi eFIFA World Cup muna 2006 na2010, akapindawo mumakwikwi eFIFA World Cup muna 2004
, 2011 uye 2015 Copa América makwikwi; muna 2011 Paraguay akapedza runners-up. Valdez akaita zvinopfuura makumi manomwe zvemitambo yenyika uye akarova zvibodzwa gumi nezvitatu, chimwe chezvinangwa zvake chichiuya mukukunda nhoroondo 1<unk>0 vachipesana nevakwikwidzi veArgentina musi wa9 Gunyana 2009 iyo yakachengetedza kukodzera kweParaguay ku2010 World Cup uye mhedzisiro yacho kuve kukunda kwechipiri kweParaguay kukunda Argentina.