 Nyora kupfuurira kweiyi ndima - Mumwaka wa1995-1996, Slutskaya akakwikwidza muchirongwa chekutanga cheChampions Series yakazotumidzwa zita rekuti ISU Grand Prix yeFigure Skating, achitora bronze pa1995 Skate America uye achiisa chechina pa1995 Trophée de France. Muna January 1996, paMakwikwi eEuropemuSofia, Bulgaria, akava mukadzi wokutanga wokuRussia kukunda zita reEurope, achiita zvitanhatu zvitatu mukutamba akasununguka kuti abvise shasha yekudzivirira kashanu Surya Bonaly. Slutskaya akakundawo Centennial paChando, achibatanidza naButyrskaya kupa Kwan kukundwa kwake chete kwemwaka. Mumakwikwi ekupedzisira eChampions Series, akaitirwa muParis mukupera kwaFebruary 1996, akapedza ari pamberi pemutambi wepasi rose Chen Lu 4th ndokutora menduru yesirivheri kumashure kwaMichelle Kwan. Muna March, akakwikwidza pa1996 World Championships muEdmonton, Canada. Wechitatu muchirongwa chipfupi, akabata chinzvimbo chake muchikamu chinotevera mushure mekupora kubva pakudonha kwekutanga kuti apedze zvitatu zvitatu. Akapiwa menduru yebronze ndokusvika paWorld podium yake yekutanga, pamwe chete naKwan munhu akawana menduru yegoridhe naChen wesirivha. 