 Nyora kuenderera kweiyi ndima - Mumwaka wa1994-95, Slutskaya akaenderera mberi nekukwira kwake; mushure mekukunda 1995 World Juniorzita munaNovember 1994 muBudapest, akatora bronze pa1995 Russian Championships kuti akwanise kupinda mukutanga kwake mukuru ISU Championship. Pa1995 European Championships, akadzoka kubva pakudonha muchirongwa chipfupi kuti aite skating yechitatu yakanakisa yemahara skating uye akakwira kusvika kune yechishanu yakazara. Akakwanisa kupinda mumakwikwi eWorlds pamwe chete nemukundi wesirivha Olga Markova, nekupedza ari pamberi pemukwikwidzi weRussia Maria Butyrskaya 7th. Pa 1995 World Championships, Slutskaya zvakare akawira mupurogiramu pfupi asi akaita matanhatu matatu muchikamu chinotevera, achipedza 5th mupachena skating uye 7th zvachose. 