Rangers face a tricky tie against Partick when they begin their defence of the Co-operative Insurance Cup, while Celtic will host Livingston.Rangers travel to Firhill in the third round hoping for a more convincing display than last season.
Walter Smith's men needed two attempts to overcome the plucky First Division side in the Scottish Cup, winning 2-0 in the replay after being held at Ibrox.
Celtic were also paired with First Division opposition in the seeded draw at Hampden on Monday and will welcome Livingston to Parkhead.
Airdrie United were rewarded for their efforts in disposing of Hearts in the last round with a difficult away tie against Dundee United.
Fellow 'giant-killers' Morton - who overcame Hibernian - will play host to another SPL side, Inverness Caledonian Thistle.
Draw in full:
Dundee United v Airdrie United
Partick v Rangers
Motherwell v Hamilton
Morton v Inverness
Falkirk v Queen of the South
Celtic v Livingston
Dunfermline v St Mirren
Ties to be played on September 23/24.
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