League Cup: Celtic meet Kilmarnock, Dundee derby, Rangers host Dunfermline
Celtic will start the defence of the League Cup at home to Kilmarnock.
Dundee and Dundee United will meet again after being drawn together in the second round, having met at the first-round group stage on Sunday.
Last year's finalists Aberdeen visit Hamilton Academical, Rangers host Dunfermline Athletic and Hibernian take on Ayr United.
St Johnstone meet Partick Thistle, Motherwell are at Ross County and Falkirk face Livingston.
The ties will be played on 8 and 9 August.
Celtic, Aberdeen, Rangers and St Johnstone all enter the competition in round two after featuring in European competition earlier this season.
They were seeded along with four of the first-round group winners - Ayr, Dundee United, Motherwell and Falkirk - when the draw was made at Dens Park.
Earlier at Dundee's home ground, Neil McCann's side drew 1-1 with city rivals United but lost the bonus-point penalty shoot-out.
That 4-3 victory on spot-kicks ensured Ray McKinnon's United took top spot in Group C and the last seeded place in the second-round draw.
Dundee manager Neil McCann said he got his wish of another derby against their city rivals.
"When I went into the dressing room it was quiet and I said 'I want another crack at them'," he said.
"We got one, that's why there was a cheer going up. That's not being disrespectful or arrogant, it's just a fantastic game to be involved in."
Dundee United manager Ray McKinnon feels his side will be in better shape by the time they return to Dens Park.
He said: "I would rather it was at Tannadice, but listen, they have nothing to fear coming here.
"It will be a tough game again, Dundee are a good side, but we have shown we can go out there and play.
"And hopefully we will have James Keatings. Scott McDonald will have had another 10 days' training, Willo Flood has only had one game, 60 minutes, with the kids. If we can get these people back fit we will come back here with a stronger squad."
St Johnstone v Partick Thistle
Hibernian v Ayr United
Rangers v Dunfermline Athletic
Ross County v Motherwell
Falkirk v Livingston
Hamilton Academical v Aberdeen
Celtic v Kilmarnock
Dundee v Dundee United
Ties to be played on 8/9 August