 Ramba uchiverenga ndima iyi - Olsen aiva kaputeni wechikwata cheDenmark chakarova muEuropean Championship muna 1984; Kupinda kwokutanga kweDenmark mumutambo wenyika dzakawanda kubvira paMitambo yeOlympic ya1972. Denmark yakasvika kumasemi-fainari, isati yabviswa neSpain pakurova kwechirango. Muna Gumiguru 1985, Olsen akava wechipiri Danish, pashure Per Røntved, kutamba 75 National chikwata machisi. Akatungamira Denmark pa 1986 World Cup, Denmark yekutanga World Cup kutora chikamu, iyo yakaguma mukukunda kwechipiri kuSpain. Kuedza kukuru kwaOlsen pamutambo uyu kwakauya mukukunda 2-0 muchikamu cheboka vachipesana neWest Germany. Akatora bhora kubva muhafu yake uye akaita dribbling run isingadzivisiki iyo yakangomiswa nechikanganiso munzvimbo yechirango cheWest Germany, naJesper Olsen achihwina chibodzwa che10 pachikanda chechirango. Olsen akazivikanwa somumwe wevatambi vakanyanya kuita paWorld Cup, uye akazotumidzwa zita ra1986 Danish Player of the Year. 