 Rambai muchinyora ndima iyi - Pa1997 ICC Trophy, Eames akatamba zvakare mumitambo yese yeHong Kong, uye akaiswa pachinzvimbo chechishanu pakumhanya pakati pevaaitamba navo, achihwina 136 kubva pamatanho masere. Chiverengero chake chepamusoro-soro, 33, chakauya mukurwisana nePapua New Guinea. Kwemitambo miviri pa2000 ACC Trophy, Eames akaendeswa kumusoro kurongeka kuti atange kurova, achihwina gumi nerimwe kumhanya kurwisa Malaysia uye matatu kumhanya kurwisa United Arab Emirates UAE. Gore rakatevera, akaonekwa muchikamu chechitatu chakateedzana cheICC Trophy, achiratidza mumitambo mina uye achiwana 45 kubva pamabhora makumi mana nemana achipesana nePapua New Guinea chikamu chehukama hwe120-run naRahul Sharma. Muna 2004, Eames akamiririra Hong Kong muACC Fast Track Countries Tournament, kuburikidza nechikwata chakakwanisa kuenda ku2005 Intercontinental Cup. Pazera remakore makumi matatu nemapfumbamwe, akaonekwa mumutambo weIntercontinental Cup uchipesana neUAE muna Kubvumbi 2005, iyo yakabata chinzvimbo chekutanga. Mitambo yake yekupedzisira yeHong Kong yakauya aine makore makumi mana nerimwe, mu2007 World Cricket League Chikamu Chechitatumutambo. 