 Miller immediately became an important player for Celtic after making his debut against Dundee, scoring the third goal of a 5–0 victory.Playing as a right winger providing chances for forwards such as Mark McGhee and fellow new signings Andy Walker and Frank McAvennie, the side won the league and Scottish Cup double in 1987–88, their centenary season; Miller has described this as his "best memory".Celtic failed to keep their grip on the league title in 1989, dropping to 3rd place as Old Firm rivals Rangers began what would be a period of dominance, and were also eliminated from the European Cup by Werder Bremen.