 Nyora kupfuurira kweiyi ndima - Kwemwaka wa1998-1999, mhedzisiro yakanakisa yaDavis yaive yekusvika kumaquarter-fainari ku1998 UK Championship, nguva yokutanga yaakanga afambira mberi kupfuura kutenderera kwechitatu mumakore mashanu, asi akarasikirwa naPaul Hunter. Akasvikawo padanho rimwechete pa1999 Welsh Open, asi akarasikirwa naWilliams. Zvisinei, pa1999 World Snooker Championship, akakundikana kukunda mutambo, achirasikirwa mumutambo wokutanga pachigadziro chisarudzo kuna Joe Perry. Akasvika kumaquarter-finals e1999 British Open muna 19992000, asi akakunda mutambo mumwe chete pa2000 World Snooker Championship, achikunda Graeme Dott, asi achirasikirwa naHiggins 1113. Mushure mekurasikirwa uku, Davis akawira kunze kwepamusoro 16 munyika yepasirese mwaka wa2000-01 kekutanga kubvira 1980 uye aisazotamba muMasters kekutanga kubva paakatanga kukodzera. 