 Nyorai kuenderera mberi kweiyi ndima - Mumwaka wa1999 kusvika 2000, Stevens akapinda mumakwikwi ose matatu ekupedzisira emakwikwi eTriple Crown. Mumakwikwi ekupedzisira e1999 UK Championship akarasikirwa naMark Williams 8-10. Akakunda zita reMasters ra2000, nekukunda Ken Doherty 10-8 mufainari. Mumakwikwi e2000 World Championship, akasvika pakupedzisira kwekutanga kwemakwikwi ake maviri epasi rose kusvika parizvino. Mushure mekukunda Tony Drago, Alan McManus, Jimmy White, naJoe Swail, akatarisana naMark Williams mumutambo wekupedzisira, achirasikirwa ne1618, mushure mekutungamira 106, 137, uyezve 1410, nechikamu chekupedzisira chekutamba. Stevens akava mutambi wechipiri chete munhoroondo yemakwikwi enyika kuti akundwe mumutambo wokupedzisira kubva pakuva nechinzvimbo chemafirimu mana usiku hwose. Akarohwawo mumakwikwi epasi rose semi-fainari kanokwana kana: muna 2001, 2002, 2004, uye 2012. Muna 2002, aiita kunge akahwina nzvimbo mumutambo wekupedzisira, achitungamira Peter Ebdon 1614 mumutambo wavo wekupedzisira, uye achingoda tsvuku yakapusa mu 31st furemu kusiya muvengi wake achida snookers. Apo Stevens akarasikirwa nepoto, Ebdon akaita kujekesa kunoshamisa kuti akunde chimiro uye akaenderera mberi kutora mafuremu maviri anotevera kuti akunde mutambo 1716. 